Hostname: page-component-6bf8c574d5-t27h7 Total loading time: 0 Render date: 2025-02-24T06:34:53.656Z Has data issue: false hasContentIssue false
  • English
  • Français

Integral modular forms and summation formulae

Published online by Cambridge University Press:  24 October 2008

A. P. Guinand
A. P. Guinand
Affiliation:
New CollegeOxford
Get access Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 43 , Issue 1 , January 1947 , pp. 127 - 129
Copyright
Copyright © Cambridge Philosophical Society 1947

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

* Guinand, A. P., Quart J. Math. 9 (1938), 53–67CrossRefGoogle Scholar, Theorem 2 with R 0(x) = 0. A(1 − s) should be substituted for A(s) in the formula (4·1).

† Rankin, R. A., Proc. Cambridge Phil. Soc. 36 (1940), 150–1.CrossRefGoogle Scholar

‡ Wilton, J. R., Proc. Cambridge Phil. Soc. 25 (1928), 121–9.CrossRefGoogle Scholar

* Titchmarsh, E. C., Fourier Integrals (Oxford, 1937), 196.Google Scholar

† Guinand, A. P., Annals of Math. 42 (1941), 591–603CrossRefGoogle Scholar, Lemma 4. The present lemma is proved in the same way. We use the notation

‡ Loc. cit.

* A. P. Guinand, Quart. J. Math. loc. cit. Theorem 1. The dashes indicate that the terms n = x are to be halved if x is an integer.

† See E. C. Titchmarsh, loc. cit. pp. 265–7, where the method is applied to a similar problem.

‡ Hardy, G. H., Proc. Cambridge Phil. Soc. 34 (1938), 309–15.CrossRefGoogle Scholar

§ Walfisz, A., Math. Ann. 108 (1933), 75–90.CrossRefGoogle Scholar