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Arithmetical identities and Hecke's functional equation

Published online by Cambridge University Press:  20 January 2009

Bruce C. Berndt
Affiliation:
University of Illinois, Urbana, Illinois
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Extract

We consider a subclass of the Dirichlet series studied by Chandrasekharan and Narasimhan in (1). Our objective is to generalize some identities due to Landau (3) concerning r2(n), the number of representations of the positive integer n as the sum of 2 squares. We shall also give a slight extension of Theorem III in (1).

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1969

References

(1)Chandrasekharan, K. and Narasimhan, RaghavanHecke's functional equation and arithmetical identities, Ann. of Math. (2) 74 (1961), 123.CrossRefGoogle Scholar
(2)Hardy, G. H.A further note on Ramanujan's arithmetical function τ(n), Proc. Cambridge Philos. Soc. 34 (1938), 309315.CrossRefGoogle Scholar
(3)Landau, EdmundVorlesungen über Zahlentheorie, Zweiter Band (S. Hirzel, Leipzig 1927).Google Scholar
(4)Rankin, R. A.Contribution to the theory of Ramanujan's function τ(n) and similar arithmetical functions, Proc. Cambridge Philos. Soc. 36 (1940), 150151.CrossRefGoogle Scholar
(5)Watson, G. N.Theory of Bessel Functions, 2nd ed. (Cambridge, 1944).Google Scholar
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