Average values of symmetric square $L$-functions at the edge of the critical strip
نویسندگان
چکیده
منابع مشابه
Distribution of Values of L-functions at the Edge of the Critical Strip
Abstract. We prove several results on the distribution of values of L-functions at the edge of the critical strip, by constructing and studying a large class of random Euler products. Among new applications, we provide a precise estimate for the distribution of the values at s = 1 of the family of k-th symmetric power L-functions of primitive cusp forms of weight 2 in the level aspect (assuming...
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Let Lsym2(f)(s) be the symmetric square L-function associated to a newform of weight 2 and level N . For N prime, we will derive asymptotic formulae for the average values of Lsym2(f)(s) at a general point on the line Re(s) = 2 when f varies over the set of all normalized newforms. RÉSUMÉ: Soit Lsym2(f)(s) la fonction L du carré symétrique d’une forme primitive de poids 2 et niveau N . Pour N p...
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Critical Values of Symmetric Power L-functions
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(Under the Riemann Hypothesis the stronger bound |ζ(1 + it)| ≥ c log log t holds.) From a modern point of view, the method of de la Vallée Poussin is based on Rankin-Selberg convolutions and a positivity argument (an effective version of Landau’s Lemma – see [HL94, Appendix]). It can be applied to any Rankin-Selberg L-function L(s, π1 ⊗ π2), provided that one of the πi’s is self-dual (cf. [Sar0...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06725-4