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Integral modular forms and summation formulae

Published online by Cambridge University Press:  24 October 2008

A. P. Guinand
A. P. Guinand
Affiliation:
New CollegeOxford
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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

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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