Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-13T08:01:37.275Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  31 August 2022

Jan-Hendrik Evertse
Affiliation:
Universiteit Leiden
Kálmán Győry
Affiliation:
Debreceni Egyetem, Hungary
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aschenbrenner, M. (2000), Ideal membership in polynomial rings over the integers, J. Amer. Math. Soc. 17, 407-442.Google Scholar
Baker, A. (1969), Linear forms in the logarithms of algebraic numbers, Mathematika 13, 204-216.Google Scholar
Baker, A. (1969a), Linear forms in the logarithms of algebraic numbers, II, Mathematika 14, 102-107.CrossRefGoogle Scholar
Baker, A. (1969b), Linear forms in the logarithms of algebraic numbers, III, Mathematika 14, 220-228.Google Scholar
Baker, A. (1969a), Linear forms in the logarithms of algebraic numbers, IV, Mathematika 15, 204-216.CrossRefGoogle Scholar
Baker, A. (1969b), Contributions to the theory of Diophantine equations, Philos. Trans.Google Scholar
Roy. Soc. London. Ser. A 263, 173-208.Google Scholar
Baker, A. (1969c), The Diophantine equation y2 = ax3 + bx2 + cx + d, J. London Math. Soc. 43, 1-9.Google Scholar
Baker, A. (1969), Bounds for the solutions of the hyperelliptic equation, Proc. Camb.Google Scholar
Philos. Soc. 65, 439-444.Google Scholar
Baker, A. (1979), Transcendental Number Theory, Cambridge University Press.Google Scholar
Baker, A., ed. (1989), New Advances in Transcendence Theory, Cambridge University Press.Google Scholar
Baker, A. and Coates, J. (1979), Integer points on curves ofgenus 1, Proc. Camb. Philos. Soc. 67, 595-602.CrossRefGoogle Scholar
Baker, A. and Masser, D. W., eds. (1979), Transcendence Theory: Advances and Applications, Academic Press.Google Scholar
Baker, A. and Wüstholz, G. (2000), Logarithmic Forms and Diophantine Geometry, Cambridge University Press.Google Scholar
Bennett, M. A. and Skinner, C.S. (2000), Ternary Diophantine equations via Galois representations and modular forms, Canad. J. Math. 56, 23-54.CrossRefGoogle Scholar
Bérczes, A. (2010a), Effective results for unit points on curves over finitely generated domains, Math. Proc. Camb. Philos. Soc. 158, 331-353.Google Scholar
Bérczes, A. (2010b), Effective results for division points on curves in, J. Théorie Nombres Bordeaux 27, 405-437.CrossRefGoogle Scholar
Bérczes, A., Evertse, J.-H., and Gyory, K. (2000), Effective results for linear equations in two unknowns from a multiplicative division group, Acta Arith. 136, 331-349.Google Scholar
Bérczes, A., Evertse, J.-H., and Gyory, K. (2010), Effective results for hyper- and superel- liptic equations over number fields, Publ. Math. Debrecen 82, 727-756.Google Scholar
Bérczes, A., Evertse, J.-H., and Gyory, K. (2010), Effective results for Diophantine equations over finitely generated domains, Acta Arith. 163, 71-100.Google Scholar
Bérczes, A., Evertse, J.-H., Gyory, K., and Pontreau, C. (2000), Effective results for points on certain subvarieties of a tori, Math. Proc. Camb. Phil. Soc. 147, 69-94.Google Scholar
Bilu, Yu. F. (1999), Effective analysis of integral points on algebraic curves, Israel J. Math. 90, 235-252.Google Scholar
Birch, B. J. and Merriman, J.R. (1979), Finiteness theorems for binary forms with given discriminant, Proc. London Math. Soc. (3) 24, 385-394.Google Scholar
Bombieri, E. (1999), Effective Diophantine approximation on Gm, Ann. Scuola Norm. Sup. Pisa (IV) 20, 61-89.Google Scholar
Bombieri, E. and Cohen, P.B. (1999), Effective Diophantine approximation on Gm, II, Ann. Scuola Norm. Sup. Pisa (IV) 24, 205-225.Google Scholar
Bombieri, E. and Cohen, P.B. (2000), An elementary approach to effective Diophantine approximation on Gm, in: Number Theory and Algebraic Geometry, Cambridge University Press, pp. 41-62.Google Scholar
Bombieri, E. and Gubler, W. (2000), Heights in Diophantine Geometry, Cambridge University Press.Google Scholar
Borevich, Z. I. and Shafarevich, I.R. (1969), Number Theory, 2nd ed., Academic Press.Google Scholar
Borosh, I., Flahive, M., Rubin, D., and Treybig, B. (1989), A sharp bound for solutions of linear Diophantine equations, Proc. Amer. Math. Soc. 105, 844-846.Google Scholar
Brindza, B. (1989), On S-integral solutions of the equation ym = f (x), Acta Math. Hungar. 44, 133-139.Google Scholar
Brindza, B. (1989), On S-integral solutions of the Catalan equation, Acta Arith. 48, 397-412.CrossRefGoogle Scholar
Brindza, B. (1989), On the equation f ( x ) = yn over finitely generated domains, Acta Math. Hungar. 53, 377-383.Google Scholar
Brindza, B. (1999), The Catalan equation over finitely generated integral domains, Publ. Math. Debrecen 42, 193-198.Google Scholar
Brindza, B., Gyory, K., and Tijdeman, R. (1989), On the Catalan equation over algebraic number fields, J. Reine Angew. Math. 367, 90-102.Google Scholar
Brownawell, W. D. and Masser, D.W. (1989), Vanishing sums in function fields, Math. Proc. Camb. Phil. Soc. 100, 427-434.Google Scholar
Bugeaud, Y. (1999), Bornes effectives pour les solutions des équations en S-unités et des équations de Thue-Mahler, J. Number Theory 71, 227-244.Google Scholar
Bugeaud, Y. (2010), Linear Forms in Logarithms and Applications, European Mathematical Society.Google Scholar
Bugeaud, Y. and Gyory, K. (1999a), Bounds for the solutions of unit equations, Acta Arith. 74, 67-80.CrossRefGoogle Scholar
Bugeaud, Y. and Gyory, K. (1999b), Bounds for the solutions of Thue-Mahler equations and norm form equations, Acta Arith. 74, 273-292.Google Scholar
Cassels, J.W.S. (1959), An Introduction to the Geometry of Numbers, Springer.CrossRefGoogle Scholar
Catalan, E. (1848), Note extraite d’une lettre adressée àl’éditeur, J. Reine Angew. Math. 27, 192.Google Scholar
Coates, J. (1969), An effective p-adic analogue of a theorem ofThue, Acta Arith. 15, 279-305.CrossRefGoogle Scholar
Dobrowolski, E. (1979), On a question ofLehmer and the number of irreducible factors of a polynomial, Acta Arith. 34, 391-401.Google Scholar
Dvornicich, R. and Zannier, U. (1999), A note on Thue’s equation over function fields, Monatsh. Math. 118, 219-230.Google Scholar
Evertse, J.-H. (1989), Upper bounds for the numbers of solutions of Diophantine equations, PhD thesis, Leiden University. Also published as Math. Centre Tracts No. 168, CWI, Amsterdam.Google Scholar
Evertse, J.-H. (1989), On sums of S-units and linear recurrences, Compos. Math. 53, 225-244.Google Scholar
Evertse, J.-H. and Gyory, K. (1989a), On the number of solutions of weighted unit equations, Compos. Math. 66, 329-354.Google Scholar
Evertse, J.-H. and Gyory, K. (1989b), Finiteness criteria for decomposable form equations, Acta Arith. 50, 357-379.Google Scholar
Evertse, J.-H. and Gyory, K. (2010), Effective results for unit equations over finitely generated integral domains, Math. Proc. Camb. Phil. Soc. 154, 351-380.Google Scholar
Evertse, J.-H. and Gyory, K. (2010), Effective results for Diophantine equations over finitely generated domains: A survey, in: Turan Memorial, Number Theory, Analysis and Combinatorics, (Pintz, J., Biro, A., Györy, K., Harcos, G., Simonovits, M., and Szabados, J., eds.). De Gruyter, 63-74.Google Scholar
Evertse, J.-H. and Gyory, K. (2010), Unit Equations in Diophantine Number Theory, Cambridge University Press.Google Scholar
Evertse, J.-H. and Gyory, K. (2010a), Discriminant Equations in Diophantine Number Theory, Cambridge University Press.Google Scholar
Evertse, J.-H. and Gyory, K. (2010b), Effective results for discriminant equations over finitely generated integral domains, in: Number Theory, Diophantine Problems, Uniform Distribution and Applications (Elsholtz, C. and Grabner, P., eds.). Springer, 237-256.Google Scholar
Evertse, J.-H., Gyory, K., Stewart, C. L., and Tijdeman, R. (1989a), On S-unit equations in two unknowns, Invent. Math. 92, 461-477.CrossRefGoogle Scholar
Evertse, J.-H., Gyory, K., Stewart, C. L., and Tijdeman, R. (1989b), S-unit equations and their applications, in: New Advances in Transcendence Theory, Proc. Conf. Durham 1986 (Baker, A., ed.). Cambridge University Press, 110-174.Google Scholar
Faltings, G. (1989), Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73, 349-366, Erratum: ibid. 75 (1989), 381.Google Scholar
Faltings, G. and Wüstholz, G. (1989), Rational points, Seminar Bonn/Wuppertal 1983/84, Aspects. Math. E6, Vieweg.Google Scholar
Feldman, N. I. and Nesterenko, Y.V. (1999), Transcendental Numbers, Springer Verlag. Vol. 44 of Encyclopaedia of Mathematical Sciences.Google Scholar
Le Fourn, S. (2020), Tubular approaches to Baker’s method for curves and varieties, Algebra Number Theory 14, 763-785.Google Scholar
Freitas, N., Kraus, A., and Siksek, S. (2020a), On the unit equation over cyclic number fields of prime degree, arXiv:2012.06445v1 [math.NT] 11 December 2020.Google Scholar
Freitas, N., Kraus, A., and Siksek, S. (2020b), On local criteria for the unit equation and the asymptotic Fermat’s last theorem, arXiv:2012.12666v1 [math.NT] 23 December 2020.Google Scholar
Friedman, E. (1989), Analytic formulas for regulators of number fields, Invent. Math. 98, 599-622.CrossRefGoogle Scholar
Gel’fond, A. O. (1939), Sur le septième problème de Hilbert, Izv. Akad. Nauk SSSR 7, 623-630.Google Scholar
Gel’fond, A. O. (1939), On approximating transcendental numbers by algebraic numbers, Dokl. Akad. Nauk SSSR 2, 177-182.Google Scholar
Gyory, K. (1979), Sur l’irreducibilité d’une classe des polynômes II., Publ. Math. Debrecen 19, 293-326.Google Scholar
Gyory, K. (1979), Sur les polynômes à coefficients entiers et de discriminant donné, Acta Arith. 23, 419-426.Google Scholar
Gyory, K. (1979), Sur les polynômes à coefficients entiers et de discriminant donné II, Publ. Math. Debrecen 21, 125-144.Google Scholar
Gyory, K. (1979), Sur les polynômes à coefficients entiers et de discriminant donné III, Publ. Math. Debrecen 23, 141-165.CrossRefGoogle Scholar
Gyory, K. (1979a), On polynomials with integer coefficients and given discriminant IV, Publ. Math. Debrecen 25, 155-167.Google Scholar
Gyory, K. (1979b), On polynomials with integer coefficients and given discriminant V, P-adic generalizations, Acta Math. Acad. Sci. Hungar. 32, 175-190.Google Scholar
Gyory, K. (1979), On the number of solutions of linear equations in units of an algebraic number field, Comment. Math. Helv. 54, 583-600.CrossRefGoogle Scholar
Gyory, K. (1989a), Explicit upper bounds for the solutions of some Diophantine equations, Ann. Acad. Sci. Fenn. Ser. A I. Math. 5, 3-12.Google Scholar
Gyory, K. (1989b), Résultats effectifs sur la représentation des entiers par des formes désomposables, Queen’s Papers in Pure and Applied Math., No. 56, Kingston, Canada.Google Scholar
Gyory, K. (1989a), On S-integral solutions of norm form, discriminant form and index form equations, Studia Sci. Math. Hungar. 16, 149-161.Google Scholar
Gyory, K. (1989b), On discriminants and indices of integers of an algebraic number field, J. Reine Angew. Math. 324, 114-126.Google Scholar
Gyory, K. (1989), On certain graphs associated with an integral domain and their applications to Diophantine problems, Publ. Math. Debrecen 29, 79-94.Google Scholar
Gyory, K. (1989), Bounds for the solutions of norm form, discriminant form and index form equations infinitely generated integral domains, Acta Math. Hungar. 42, 45-80.CrossRefGoogle Scholar
Gyory, K. (1989a), On norm form, discriminant form and indexform equations, in: Topics in Classical Number Theory (Baker, A., ed.). North-Holland Publ. Comp., 617676.Google Scholar
Gyory, K. (1989b), Effective finiteness theorems for polynomials with given discriminant and integral elements with given discriminant over finitely generated domains, J. Reine Angew. Math. 346, 54-100.Google Scholar
Gyory, K. (1999), On arithmetic graphs associated with integral domains, in: A Tribute to Paul Erdos (Baker, A., Bollobas, B. and Hajnal, A., eds.). Cambridge University Press, 207-222.Google Scholar
Gyory, K. (1999), Some recent applications of S-unit equations, Astérisque 209, 17-38.Google Scholar
Gyory, K. (1999), On the numbers of families of solutions of systems of decomposable form equations, Publ. Math. Debrecen 42, 65-101.Google Scholar
Gyory, K. (1999), Bounds for the solutions of decomposable form equations, Publ. Math. Debrecen 52, 1-31.Google Scholar
Gyory, K. (2000), Solving Diophantine equations by Baker’s theory, in: A Panorama of Number Theory (Wüstholz, G., ed.). Cambridge University Press, 38-72.Google Scholar
Gyory, K. (2010), Bounds for the solutions of S-unit equations and decomposable form equations II, Publ. Math. Debrecen 94, 507-526.CrossRefGoogle Scholar
Gyory, K. and Papp, Z.Z. (1979), On discriminant form and index form equations, Studia Sci. Math. Hungar. 12, 47-60.Google Scholar
Gyory, K. and Papp, Z.Z. (1979), Effective estimates for the integer solutions of norm form and discriminant form equations, Publ. Math. Debrecen 25, 311-325.Google Scholar
Gyory, K. and Yu, K. (2000), Bounds for the solutions of S-unit equations and decomposable form equations, Acta Arith. 123, 9-41.Google Scholar
Hartshorne, R. (1979), Algebraic Geometry, Springer Verlag.Google Scholar
Hermann, G. (1929), Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95, 736-788.Google Scholar
de Jong, T. (1999), An algorithm for computing the integral closure, J. Symb. Comput. 26, 273-277.Google Scholar
von Känel, R. (2010), Modularity and integral points on moduli schemes, arXiv: 1310.7263v2 [math.NT].Google Scholar
von Känel, R. and Matschke, B. (2010), Solving S-unit, Mordell, Thue, Thue-Mahler and generalized Ramanujan-Nagell equations via Shimura-Taniyama conjecture, arXiv:1605.06079.Google Scholar
Kim, D. (2010), A modular approach to cubic Thue-Mahler equations, Math. Comp. 86, 1435-1471.Google Scholar
Kotov, S. V. and Sprindzuk, V.G. (1979), An effective analysis of the Thue-Mahler equation in relative fields, Dokl. Akad. Nauk BSSR 17, 393-395 (Russian).Google Scholar
Kotov, S. V. and Trelina, L.A. (1979), S-ganze Punkte auf elliptischen Kurven, J. Reine Angew. Math. 306, 28-41.Google Scholar
Koymans, P. (2010), The Catalan equation, Master thesis, Leiden University.Google Scholar
Koymans, P. (2010), The Catalan equation, Indag. Math. (N.S.) 28, 321-352.Google Scholar
Lang, S. (1969), Integral points on curves, Inst. Hautes Études Sci. Publ. Math. 6, 27-43.Google Scholar
Lang, S. (1969), Diophantine Geometry, Wiley.Google Scholar
Lang, S. (1969a), Division points on curves, Ann. Mat. Pura Appl. (4) 70, 229-234.Google Scholar
Lang, S. (1969b), Report on Diophantine approximations, Bull. Soc. Math. France 93, 177-192.Google Scholar
Lang, S. (1979), Elliptic Curves: Diophantine Analysis, Springer.Google Scholar
Lang, S. (1989), Fundamentals of Diophantine Geometry, Springer.Google Scholar
Lang, S. (1999), Algebraic Number Theory, 2nd ed., Springer.Google Scholar
Laurent, M. (1989), Équations diophantiennes exponentielles, Invent. Math. 78, 299-327.Google Scholar
LeVeque, W.J. (1969), On the equation ym = f (x), Acta Arith. 9, 209-219.Google Scholar
Liardet, P. (1979), Sur une conjecture de Serge Lang, C.R. Acad. Sci. Paris 279, 435437.Google Scholar
Liardet, P. (1979), Sur une conjecture de Serge Lang, Astérisque 24-25, Soc. Math. France, 187-210.Google Scholar
Loher, T. and Masser, D. (2000), Uniformly counting points of bounded height, Acta Arith. 111, 277-297.Google Scholar
Louboutin, S. (2000), Explicit bounds for residues of Dedekind zeta functions, values of L-functions at s = 1, and relative class numbers, J. Number Theory 85, 263-282.Google Scholar
Loxton, J. H. and van der Poorten, A.J. (1989), Multiplicative dependence in number fields, Acta Arith. 42, 291-302.Google Scholar
Mahler, K. (1939), Zur Approximation algebraischer Zahlen I: Über den grössten Primteiler binärer Formen, Math. Ann. 107, 691-730.CrossRefGoogle Scholar
Mahler, K. (1939), Über die rationalen Punkte auf Kurven vom Geschlecht Eins, J. Reine Angew. Math. 170, 168-178.Google Scholar
Mason, R.C. (1989), On Thue’s equation over function fields, London Math. Soc. 24, 414-426.Google Scholar
Mason, R.C. (1989), The hyperelliptic equation over function fields, Math. Proc. Camb. Phil. Soc. 93, 219-230.Google Scholar
Mason, R.C. (1989), Diophantine Equations over Function Fields, Cambridge University Press.Google Scholar
Mason, R.C. (1989), Norm form equations I., J. Number Theory 22, 190-207.Google Scholar
Mason, R.C. (1989), The study of Diophantine equations over function fields, in: New Advances in Transcendence Theory (Baker, A., ed.). Cambridge University Press, 229-244.Google Scholar
Matsumura, H. (1989), Commutative Ring Theory, Cambridge University Press.Google Scholar
Matsumoto, R. (2000), On computing the integral closure, Commun. Algebra 28, 401-405.CrossRefGoogle Scholar
Matveev, E.M. (2000), An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers, II. Izvestiya: Mathematics 64, 1217-1269.Google Scholar
Mihailescu, P. (2000), Primary cyclotomic units and a proof of Catalan’s conjecture, J. Reine Angew. Math. 572, 167-195.Google Scholar
Mordell, L.J. (1929a), On the rational solutions of the indeterminate equations of the third and fourth degrees, Proc. Camb. Phil. Soc. 21, 179-192.Google Scholar
Mordell, L.J. (1929b), Note on the integer solutions of the equation E y2 = Ax3 + Bx2 + Cx + D, Messenger Math. 51, 169-171.Google Scholar
Mordell, L.J. (1929), On the integer solutions of the equation e y2 = ax3 + bx2 + cx + d, Proc. London Math. Soc. (2) 21, 415-419.Google Scholar
Mordell, L.J. (1969), Diophantine Equations, Academic Press.Google Scholar
Moriwaki, A. (2000), Arithmetic height functions over finitely generated fields, Invent. Math. 140, 101-142.Google Scholar
Murty, M. R. and Pasten, H. (2010), Modular forms and effective Diophantine approximation, J. Number Theory 133, 3739-3754.Google Scholar
Nagata, M. (1959), A general theory of algebraic geometry over Dedekind domains I., Amer. J. Math. 78, 78-116.Google Scholar
Osgood, C.F. (1979), An effective lower bound on the ‘Diophantine approximation’ of algebraic functions by rational functions, Mathematika 20, 4-15.Google Scholar
Osgood, C.F. (1979), Effective bounds on the ‘Diophantine approximation’ of algebraic functions over fields of arbitrary characteristic and applications to differential equations, Indag. Math. 37, 105-119.Google Scholar
Parry, C.J. (1959), The p-adic generalization of the Thue-Siegel theorem, Acta Math. 83, 1-100.CrossRefGoogle Scholar
Pasten, H. (2010), Shimura curves and the abc conjecture, arXiv:1705.09251v1 [math.NT], 25 May 2017.Google Scholar
Poonen, B. (2010), The S-integral points on the projective line minus three points via étale covers and Skolem method. Available at https://math.mit.edu/~poonen/ papers/siegel_for_Q.pdf.Google Scholar
Roquette, P. (1959), Einheiten und Divisorenklassen in endlich erzeugbaren Körpern, Jahresber. Deutsch. Math. Verein 60, 1-21.Google Scholar
Schlickewei, H.P. (1979), On norm form equations, J. Number Theory 9, 370-380.Google Scholar
Schinzel, A. and Tijdeman, R. (1979), On the equation ym = P(x), Acta Arith. 31, 199-204.Google Scholar
Schmidt, W.M. (1979), Linearformen mit algebraischen Koeffizienten II, Math. Ann. 191, 1-20.Google Scholar
Schmidt, W.M. (1979), Norm form equations, Ann. Math. 96, 526-551.Google Scholar
Schmidt, W.M. (1979), On Osgood’s effective Thue theorem for algebraic functions, Commun. Pure Applied Math. 29, 759-773.Google Scholar
Schmidt, W.M. (1979), Thue’s equation over function fields, J. Austral. Math. Soc. Ser A 25, 385-422.Google Scholar
Schmidt, W.M. (1999), Diophantine Approximations and Diophantine Equations, Lecture Notes Math. 1467, Springer.Google Scholar
Schneider, T. (1939), Transzendenzuntersuchungen periodischer Funktionen: I Transzendenz von Potenzen; II Transzendenzeigenschaften elliptischer Funktionen, J. Reine Angew. Math. 172, 65-74.Google Scholar
Seidenberg, A. (1979), Constructions in algebra, Trans. Amer. Math. Soc. 197, 273-313.Google Scholar
Shorey, T. N. and Tijdeman, R. (1989), Exponential Diophantine Equations, Cambridge University Press.Google Scholar
Siegel, C.L. (1929), Approximation algebraischer Zahlen, Math. Z. 10, 173-213.CrossRefGoogle Scholar
Siegel, C.L. (1929), The integer solutions of the equation y2 = axn + bxn-1 + ••• + k, J. London Math. Soc. 1, 66-68.Google Scholar
Siegel, C.L. (1929), Über einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss., Phys. Math. Kl., No. 1.Google Scholar
Siksek, S. (2010), Explicit Chabauty over number fields, Algebra Number Theory 7, 765-793.Google Scholar
Simmons, H. (1979), The solution of a decision problem for several classes of rings, Pacific J. Math. 34, 547-557.Google Scholar
Smart, N.P. (1999), The Algorithmic Resolution of Diophantine Equations, Cambridge University Press.Google Scholar
Sprindzuk, V.G. (1989), Classical Diophantine Equations in Two Unknowns (Russian), Nauka, Moskva.Google Scholar
Sprindzuk, V.G. (1999), Classical Diophantine Equations, Lecture Notes Math. 1559, Springer.Google Scholar
Stark, H.M. (1979), Some effective cases of the Brauer-Siegel theorem, Invent. Math. 23, 135-152.CrossRefGoogle Scholar
Stothers, W.W. (1989), Polynomial identities and Hauptmodulen, Quart. J. Math., Oxford Ser. (2) 32, 349-370.Google Scholar
Thue, A. (1909), Über Annäherungswerte algebraischer Zahlen, J. Reine Angew. Math. 135, 284-305.Google Scholar
Tijdeman, R. (1979), On the equation of Catalan, Acta Arith. 29, 197-209.CrossRefGoogle Scholar
Triantafillou, N. (2020), The unit equation has no solutions in number fields of degree prime to 3 where 3 splits completely, arXiv:2003.02414.Google Scholar
van der Poorten, A. J. and Schlickewei, H.P. (1989), The growth condition for recurrence sequences, Macquarie Univ. Math. Rep. 82-0041.Google Scholar
van der Poorten, A. J. and Schlickewei, H.P. (1999), Additive relations infields, J. Austral. Math. Soc. (Ser. A) 51, 154-170.Google Scholar
Végso, J. (1999), On superelliptic equations, Publ. Math. Debrecen 44, 183-187.Google Scholar
Voutier, P. (1999), An effective lower bound for the height of algebraic numbers, Acta Arith. 74, 81-95.Google Scholar
Waldschmidt, M. (2000), Diophantine Approximation on Linear Algebraic Groups, Springer.CrossRefGoogle Scholar
Wüstholz, G., ed. (2000), A Panorama of Number Theory or the View from Baker’s Garden, Cambridge University Press.Google Scholar
Yu, K. (2000), P-adic logarithmic forms and group varieties III, Forum Mathematicum 19, 187-280.Google Scholar
Zannier, U. (2000), Lecture Notes on Diophantine Analysis, Lecture Notes, Scuola Normale Superiore di Pisa (New Series), 8 Edizioni della Normale.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Jan-Hendrik Evertse, Universiteit Leiden, Kálmán Győry, Debreceni Egyetem, Hungary
  • Book: Effective Results and Methods for Diophantine Equations over Finitely Generated Domains
  • Online publication: 31 August 2022
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Jan-Hendrik Evertse, Universiteit Leiden, Kálmán Győry, Debreceni Egyetem, Hungary
  • Book: Effective Results and Methods for Diophantine Equations over Finitely Generated Domains
  • Online publication: 31 August 2022
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Jan-Hendrik Evertse, Universiteit Leiden, Kálmán Győry, Debreceni Egyetem, Hungary
  • Book: Effective Results and Methods for Diophantine Equations over Finitely Generated Domains
  • Online publication: 31 August 2022
Available formats
×