Identities involving the coefficients of a class of dirichlet series. vii

Research output: Contribution to journalArticlepeer-review

Abstract

Let a(n) be an arithmetical function, and consider the Riesz sum Ar(x) = Sn£xa(n)(x-n)r. For a(n) belonging to a certain class of arithmetical functions, Ar(x) can be expressed in terms of an infinite series of Bessel functions. K. Chandrasekharan and R. Narasimhan have established this identity for the widest known range of r. Their proof depends upon equi-convergence theory of trigonometric series. An alternate proof is given here which uses only the classical theory of Bessel functions.

Original languageEnglish (US)
Pages (from-to)247-261
Number of pages15
JournalTransactions of the American Mathematical Society
Volume201
DOIs
StatePublished - 1975
Externally publishedYes

Keywords

  • Arithmetical function
  • Average order of arithmetical functions
  • Bessel function identity
  • Dirichlet series
  • Functional equation involving gamma factors
  • Hardy-Landau circle method
  • Riesz sum

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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