Exceptional characters and nonvanishing of Dirichlet L-functions

Hung Bui, Kyle Pratt, Alexandru Zaharescu

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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
Pages (from-to)593-642
Number of pages50
JournalMathematische Annalen
Issue number1-2
Early online date6 Feb 2021
Publication statusPublished - Jun 2021


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