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Sir Edmund Whittaker's Work on Automorphic Functions

Published online by Cambridge University Press:  20 January 2009

R. A. Rankin
R. A. Rankin
Affiliation:
Department of Mathematics, The University Glasgow
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Although only three of Whittaker's papers (12, 13, 14) are on the theory of automorphic functions, he retained his interest in it throughout his life. His son, Dr J. M. Whittaker, informs me that his last mathematical conversation with his father was on this subject. The standard English work on automorphic functions by L. R. Ford (4), and its precursor in the Edinburgh Mathematical Tracts series, owe much to Whittaker, and it was he who suggested the term “isometric circle” of which Ford makes such elegant use in his development of the theory. Professor G. N. Watson informs me that Whittaker had expressed his willingness to contributea a chapter on automorphic functions to the revised and expanded edition of Modern Analysis which is in preparation.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 11 , Issue 1 , June 1958 , pp. 25 - 30
Copyright
Copyright © Edinburgh Mathematical Society 1958

References

REFERENCES

(1)Burnside, W., Note on the equation y 2 = x (x 4 – 1), Proc. London Math. Soc. (1), 24 (1893), 17–20.Google Scholar
(2)Dalzell, D. P., A note on automorphic functions, J. London Math. Soc., 5 (1930), 280–2.CrossRefGoogle Scholar
(3)Dhar, S. C., On the uniformisation of a special kind of algebraic curve of any genus, J. London Math. Soc., 10 (1935), 259–263.CrossRefGoogle Scholar
(4)Ford, L. R., Automorphic functions (New York, 1929).Google Scholar
(5)Hodgkinson, J., Note on the uniformization of hyperelliptic curves, J. London Math. Soc., 11 (1936), 185–192.CrossRefGoogle Scholar
(6)Klein, F. and Fricke, R., Vorlesungen über die Theorie der elliptischen Modulfunktionen (Leipzig, 1890–1892).Google Scholar
(7)Mursi, M., On the uniformisation of algebraic curves of genus 3, Proc. Edinburgh Math. Soc. (2), 2 (1930), 101–7.CrossRefGoogle Scholar
(8)Mursi, M., A note on automorphic functions, J. London Math. Soc., 6 (1931), 166–9.CrossRefGoogle Scholar
(9)Rankin, R. A., The differential equations associated with the uniformization of certain algebraic curves, Proc. Boy. Soc. Edin., A 65 (1958), 35–62.Google Scholar
(10)Schwarz, H. A., Gesammelte mathematische Ahhandlungen, vol. 2 (Berlin, 1890).CrossRefGoogle Scholar
(11)Stahl, H., Berechtigung einer Arbeit von Herrn E. T. Whittaker, Arch. Math. Phys. (3), 10 (1906), 336–7.Google Scholar
(12)Whittaker, E. T., On the connexion of algebraic functions with auto- morphic functions, Phil. Trans., 192A (1898), 1–32.Google Scholar
(13)Whittaker, E. T., Note on a function analogous to Weierstrass' sigma-function, Mess. Math., 31 (1902), 145–8.Google Scholar
(14)Whittaker, E. T., On hyperlemniscate functions, a family of automorphic functions, J. London Math. Soc., 4 (1929), 274–8.CrossRefGoogle Scholar
(15)Whittaker, J. M., The uniformisation of algebraic curves, J. London Math. Soc., 5 (1930), 150–4.CrossRefGoogle Scholar