Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T18:21:41.938Z Has data issue: false hasContentIssue false
  • English
  • Français

Arithmetical identities and Hecke's functional equation

Published online by Cambridge University Press:  20 January 2009

Bruce C. Berndt
Bruce C. Berndt
Affiliation:
University of Illinois, Urbana, Illinois
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 3 , June 1969 , pp. 221 - 226
Copyright
Copyright © Edinburgh Mathematical Society 1969

References

REFERENCES

(1)Chandrasekharan, K. and Narasimhan, RaghavanHecke's functional equation and arithmetical identities, Ann. of Math. (2) 74 (1961), 1–23.CrossRefGoogle Scholar
(2)Hardy, G. H.A further note on Ramanujan's arithmetical function τ(n), Proc. Cambridge Philos. Soc. 34 (1938), 309–315.Google 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), 150–151.Google Scholar
(5)Watson, G. N.Theory of Bessel Functions, 2nd ed. (Cambridge, 1944).Google Scholar