Lower Bounds for L-functions at the Edge of the Critical Strip
نویسندگان
چکیده
(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. [Sar03], [Mor85]). Here πi, i = 1, 2 are cuspidal automorphic representations of GLni(A), A is the ring of adèles of a number field F , and the central characters of πi’s are
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