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Li Coefficients for Automorphic L-Functions | | Jeffrey C. Lagarias
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21 Apr 2004 | | Subject: | Number Theory MSC-class: 11M26 22E55 | math.NT | | Abstract: | Xian-Jin Li gave a criterion for the Riemann hypothesis in terms of the positivity of a set of coefficients lambda_n, indexed by the integers. We define similar coefficients attached to principal automorphic L-functions over GL(N). We relate these coefficients to values of Weil’s quadratic functional for the associated automorphic representation, and deduce a Riemann hypothesis criterion in terms of positivity of the real parts of these coefficients. We determine asymptotics of the coefficients, both unconditionally and on the Riemann hypothesis, as n increases. We show the existence of an entire function of exponential type that interpolates the generalized Li coefficients at integer values. | | Source: | arXiv, math.NT/0404394 | | Services: | Forum | Review | PDF | Favorites | |
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