Zeros of combinations of the Riemann ξ-function on bounded vertical shifts

Atul Dixit, Nicolas Robles, Arindam Roy, Alexandru Zaharescu

Research output: Contribution to journalArticle

Abstract

In this paper we consider a series of bounded vertical shifts of the Riemann ξ-function. Interestingly, although such functions have essential singularities, infinitely many of their zeros lie on the critical line. We also generalize some integral identities associated with the theta transformation formula and some formulae of G.H. Hardy and W.L. Ferrar in the context of a pair of functions reciprocal in Fourier cosine transform.

Original languageEnglish (US)
Pages (from-to)404-434
Number of pages31
JournalJournal of Number Theory
Volume149
DOIs
StatePublished - Apr 1 2015

Keywords

  • Bounded vertical shifts
  • Critical line
  • Ramanujan's Lost Notebook
  • Riemann zeta-function
  • Self-reciprocal functions
  • Theta transformation formula
  • Zeros

ASJC Scopus subject areas

  • Algebra and Number Theory

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