Natural Boundaries and a Correct Notion of Integral Moments of L–functions

نویسندگان

  • Adrian Diaconu
  • Paul Garrett
  • Dorian Goldfeld
  • ADRIAN DIACONU
  • PAUL GARRETT
  • DORIAN GOLDFELD
چکیده

It is shown that a large class of multiple Dirichlet series which arise naturally in the study of moments of L–functions have natural boundaries. As a remedy we consider a new class of multiple Dirichlet series whose elements have nice properties: a functional equation and meromorphic continuation. This class suggests the correct notion of integral moments of L–functions. §

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Natural Boundaries and the Correct Notion of Integral Moments of L–functions

It is shown that a large class of multiple Dirichlet series which arise naturally in the study of moments of L–functions have natural boundaries. As a remedy we consider a new class of multiple Dirichlet series whose elements have nice properties: a functional equation and meromorphic continuation. We believe this class reveals the correct notion of integral moments of L–functions. §

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تاریخ انتشار 2009