Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T07:40:38.480Z Has data issue: false hasContentIssue false
  • English
  • Français

The evaluation in terms of Γ-functions of the periods of elliptic curves admitting complex multiplication

Published online by Cambridge University Press:  24 October 2008

I. J. Zucker
I. J. Zucker
Affiliation:
University of Surrey, Guildford
Get access Rights & Permissions [Opens in a new window]

Extract

Let

and K′ = K(k′), where k2 + k′2 = 1

with

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 1 , July 1977 , pp. 111 - 118
Copyright
Copyright © Cambridge Philosophical Society 1977

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

REFERENCES

(1)Glasser, M. L. and Wood, V. E.A closed form evaluation of the elliptic integral. Math. Comp. 25 (1971), 535–536.CrossRefGoogle Scholar
(2)Hardy, G. H.Ramanujan, chaps. 1 and 12 (Chelsea, N.Y., 1959).Google Scholar
(3)Landau, E.Vorleaung über Zahlentheorie, vol. II, p. 9 (Chelsea, N.Y., 1947).Google Scholar
(4)Ramanujan, S.Modular equations and approximations to π. Quart. J. Math. Oxford 45 (1914), 350–372.Google Scholar
(5)Selberg, A. and Chowla, S.On Epstein's zeta-function. J. ReineAngew. Math. 227 (1967), 86–110.Google Scholar
(6)Watson, G. N.Some singular moduli (I). Quart. J. Math. Oxford 3 (1932), 81–98.CrossRefGoogle Scholar
(7)Weber, H.Lehrbuch der Algebra (Brauschweig, 1908), vol. III.Google Scholar
(8)Whittaker, E. T. and Watson, G. N.Modern Analysis, 4th ed. (Cambridge University Press, 1927), chap. 22Google Scholar
(9)Zucker, I. J. and Robertson, M. M.Some properties of Dirichlet L-series. J. Phys. A: Math. Gen. 9 (1976), 1207–1214.CrossRefGoogle Scholar
(10)Zucker, I. J. and Robertson, M. M.A systematic approach to the evaluation of J. Phys. A: Math. Gen. 9 (1976), 1215–1225.CrossRefGoogle Scholar