Journal of Mathematical Sciences

, Volume 193, Issue 1, pp 136–144 | Cite as

Extreme Values of Automorphic L-Functions



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,
$$ \log \left| {L\left( {\frac{1}{2}+it,f\times f} \right)} \right|={\varOmega_{+}}\left( {{{{\left( {\frac{{\log t}}{{\log\;\log t}}} \right)}}^{1/2 }}} \right) $$
$$ \log \left| {L\left( {{\sigma_0}+it,f\times f} \right)} \right|={\varOmega_{+}}\left( {{{{\left( {\frac{{\log t}}{{\log\;\log t}}} \right)}}^{{1-{\sigma_0}}}}} \right) $$
For a fixed σ 0\( \left( {\frac{1}{2},1} \right) \). Bibliography: 15 titles.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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