The first moment of the symmetric-square L-function

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We find a twisted first moment of L (sym2 f, s) at any point s on the critical line, over a basis of weight k Hecke eigenforms f for the full modular group, as k → ∞. As a corollary we show that given any point on the critical line and large enough even k, there exists an eigenform f of weight k such that L (sym2 f, s) is nonvanishing at that point.

Original languageEnglish
Pages (from-to)259-266
Number of pages8
JournalJournal of Number Theory
Issue number2
Publication statusPublished - 1 Jun 2007


ASJC Scopus subject areas

  • Algebra and Number Theory

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