Zeros of L-functions outside the critical strip

Andrew R Booker, Frank Thorne

Research output: Contribution to journalArticle (Academic Journal)peer-review

6 Citations (Scopus)
226 Downloads (Pure)

Abstract

For a wide class of Dirichlet series associated to automorphic forms, we show that those without Euler products must have zeros within the region of absolute convergence. For instance, we prove that if ƒSk(Γ1(N)) is a classical holomorphic modular form whose L-function does not vanish for R(s)>(k+1)∕2, then ƒ is a Hecke eigenform. Our proof adapts and extends work of Saias and Weingartner, who proved a similar result for degree-1 L-functions.
Original languageEnglish
Pages (from-to)2027-2042
Number of pages16
JournalAlgebra and Number Theory
Volume8
Issue number9
Early online date28 Dec 2014
DOIs
Publication statusPublished - Dec 2014

Keywords

  • L-functions
  • Euler products
  • automorphic forms

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