Hostname: page-component-5c6d5d7d68-wtssw Total loading time: 0 Render date: 2024-08-18T02:03:36.581Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Method in Arithmetical Functions and Contour Integration

Published online by Cambridge University Press:  20 November 2018

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.

If f is a suitable meromorphic function, then by a classical technique in the calculus of residues, one can evaluate in closed form series of the form,

Suppose that a(n) is an arithmetical function. It is natural to ask whether or not one can evaluate by contour integration

(1.1)

where f belongs to a suitable class of meromorphic functions. We shall give here only a partial answer for a very limited class of arithmetical functions.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 3 , September 1973 , pp. 381 - 387
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Berndt, Bruce C., The evaluation of character series by contour integration, Publ. Elektrotehn. Fak. Univerziteta U Beogradu, Ser: Mat. Fiz. (1972), 25–29.Google Scholar
2. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers, 4th ed., Oxford Univ. Press, London, 1960.Google Scholar
3. Klee, V. L. Jr, A generalization of Eulerߣs function, Amer. Math. Monthly 55 (1948), 358–359.Google Scholar
4. Suryanarayana, D., Extensions of Dedekindߣsip-function, Math. Scand. 26 (1970), 107–118.Google Scholar