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Extreme Values of Automorphic L-Functions

Abstract

Ω-theorems for some automorphic L-functions and, in particular, for the Rankin−Selberg L-function L(s, f × f) are considered. For example, as t tends to infinity,

$$ \log \left| {L\left( {\frac{1}{2}+it,f\times f} \right)} \right|={\varOmega_{+}}\left( {{{{\left( {\frac{{\log t}}{{\log\;\log t}}} \right)}}^{1/2 }}} \right) $$

and

$$ \log \left| {L\left( {{\sigma_0}+it,f\times f} \right)} \right|={\varOmega_{+}}\left( {{{{\left( {\frac{{\log t}}{{\log\;\log t}}} \right)}}^{{1-{\sigma_0}}}}} \right) $$

For a fixed σ 0\( \left( {\frac{1}{2},1} \right) \). Bibliography: 15 titles.

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Correspondence to O. M. Fomenko.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 404, 2012, pp. 233–247.

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Fomenko, O.M. Extreme Values of Automorphic L-Functions. J Math Sci 193, 136–144 (2013). https://doi.org/10.1007/s10958-013-1442-2

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  • DOI: https://doi.org/10.1007/s10958-013-1442-2