On extremal values of Euler products

Author:

STEUDING Rasa

AMS Classification:

11M06

Keywords:

estimates for linear forms, Kronecker's approximation theorem, Selberg class

Abstract:

Let {\cal L}(s) be a polynomial Euler product, being convergent for \Re s>1. We prove, conditional on Selberg's cojecture A, that for any real \theta there are infinitely many values of s=\sigma+it with \sigma\to1+ and t\to+\infty such that \Re\{\exp(i\theta)\log {\cal L}(\sigma+it)\}\gg \log\log\log\log t, where the implicit constant depends only on {\cal L}. Moreover, for any sufficiently large T, there exist t\in[T,2T] and \sigma>1 for which the latter estimate holds.

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SteudingR-06.pdf

Vol. 1 (9), 2006