Exceptional characters and nonvanishing of Dirichlet L-functions

Hung M. Bui, Kyle Pratt, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review


Let ψ be a real primitive character modulo D. If the L-function L(s, ψ) has a real zero close to s= 1 , known as a Landau–Siegel zero, then we say the character ψ is exceptional. Under the hypothesis that such exceptional characters exist, we prove that at least fifty percent of the central values L(1 / 2 , χ) of the Dirichlet L-functions L(s, χ) are nonzero, where χ ranges over primitive characters modulo q and q is a large prime of size DO(1). Under the same hypothesis we also show that, for almost all χ, the function L(s, χ) has at most a simple zero at s= 1 / 2.

Original languageEnglish (US)
Pages (from-to)593-642
Number of pages50
JournalMathematische Annalen
Issue number1-2
StatePublished - Jun 2021

ASJC Scopus subject areas

  • General Mathematics


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