The largest gap between zeros of entire L-functions is less than 41.54

Patrick Kühn, Nicolas Robles, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

Using suitable feasible pairs and convex combinations of Selberg minorant functions, the upper bound under GRH and the Ramanujan hypothesis on the largest gap between consecutive zeros of an entire L-function in Bober, Conrey, Farmer, Fujii, Koutsoliotas, Lemurell, Rubinstein and Yoshida [2] is improved from 45.3236 to 41.54. An application about nonexistence of certain entire L-functions is also provided.

Original languageEnglish (US)
Pages (from-to)1286-1301
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume449
Issue number2
DOIs
StatePublished - May 15 2017

Keywords

  • Beurling function
  • Largest gap between zeros of L-functions
  • Selberg minorant
  • Weil explicit formula

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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