Natural boundaries of a family of dirichlet series

Alexandru Zaharescu, Mohammad Zaki

Research output: Contribution to journalArticle

Abstract

We study the natural boundary of the Dirichlet series Fq,b,H,?(s) = m,k?1 mk?b (mod q) H(? log(m + k)) ?(m)?(k) (m + k)s , where ? is the classical Von Mangoldt function, H is a smooth periodic function with period 1, ? > 0 is a real number and b, q > 0 are integers with (b, q) = 1.

Original languageEnglish (US)
Pages (from-to)661-676
Number of pages16
JournalRocky Mountain Journal of Mathematics
Volume43
Issue number2
DOIs
StatePublished - Jul 10 2013

Keywords

  • Analytic continuation
  • Dirichlet series
  • Zeta and L-functions

ASJC Scopus subject areas

  • Mathematics(all)

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