Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-11T02:19:24.932Z Has data issue: false hasContentIssue false
  • English
  • Français

Distribution of rational points on varieties over finite fields

Published online by Cambridge University Press:  26 February 2010

Masahiko Fujiwara
Masahiko Fujiwara
Affiliation:
Department of Mathematics, Ochanomizu University, Otsuka Bunkyoku Tokyo, Japan.
Get access

Extract

Throughout the paper, let

be forms with rational integer coefficients of degrees d1, …, ds all at least 2 with n ≥ 4. Let p be a prime and Q a box in ℝn,

Type
Research Article
Information
Mathematika , Volume 35 , Issue 2 , December 1988 , pp. 155 - 171
Copyright
Copyright © University College London 1988

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

1.Baker, R. C.. Small solutions of congruences. Mathematika, 30 (1983), 164–188.Google Scholar
2.Baker, R. C.. Diophantine Inequalities (Oxford, 1986).Google Scholar
3.Birch, B. J.. Homogeneous forms of odd degree in a large number of variables. Mathematika, 4 (1957), 102–105.CrossRefGoogle Scholar
4.Cassels, J. W. S. and Fröhlich, A.. Algebraic number theory (Academic Press, London, 1967).Google Scholar
5.Cohen, S. D.. The distribution of galois groups and Hilbert irreducibility theorem. Proc. London Math. Soc. (3), 43 (1981), 227–250.Google Scholar
6.Deligne, P.. La conjecture de Weil I. Publ. Math. IHES., 43 (1973), 273–307.Google Scholar
7.Fujiwara, M.. Upper bounds for the number of lattice points on hypersurfaces. Number Theory and Combinatorics, edit, by Akiyama, et al. (World Sci. Publ., Hong Kong, 1985), 89–96.Google Scholar
8.Hartshorne, R.. Algebraic geometry (Springer, New York, 1977).Google Scholar
9.Heath-Brown, D. R.. Cubic forms in 10 variables. Proc. London Math. Soc. (3), 47 (1983), 225–257.Google Scholar
10.Lang, S. and Weil, A.. Number of points on varieties in finite fields. Amer. J. Math., 76 (1954), 819–827.Google Scholar
11.Lang, S.. Fundamentals of Diophantine Geometry (Springer, New York, 1983).CrossRefGoogle Scholar
12.Meyerson, G.. The distribution of ratoinal points on varieties defined over a finite field. Mathematika, 28 (1981), 153–159.Google Scholar
13.Schmidt, W. M.. Equations over finite fields: an elementary approach; Lecture Notes in Math. 536 (Springer, Berlin, 1976).Google Scholar
14.Schmidt, W. M.. Analytische Methoden für Diophantische Gleichungen. DMV Seminar Band 5 (Birkhäuser, 1984).Google Scholar
15.Schmidt, W. M.. Small solutions of congruences. Diophantiine Analysis, edit, by Loxton, J. H., Van der Poorten, A. J. (Cambridge University Press, 1986).Google ScholarPubMed
16.Schmidt, W. M.. Integer points on hypersurfaces. Mh. Math., 102 (1986), 27–58.Google Scholar
17.Vaughan, R. C.. On Waring's problem for cubes. J. reine angew. Math., 365 (1986), 122–170.Google Scholar
18.Van der Waerden, B. L.. Moder Algebra, Volume II (Frederick Ungar Publ. Co., New York 1950).Google Scholar