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Zap. Nauchn. Sem. POMI, 2012, Volume 404, Pages 233–247 (Mi znsl5271)  

This article is cited in 2 scientific papers (total in 2 papers)

Extreme values of automorphic $L$-functions

O. M. Fomenko

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We treat $\Omega$-theorems for some automorphic $L$-functons, and for the Rankin–Selberg $L$-function $L(s,f\times f)$ in particular.
For example, as $t$ tends to infinity,
$$ \log|L(\frac12+it,f\times f)|=\Omega_+((\frac{\log t}{\log\log t})^{1/2}), $$
and
$$ \log|L(\sigma_0+it,f\times f)|=\Omega_+((\frac{\log t}{\log\log t})^{1-\sigma_0}) $$
for fixed $\sigma_0\in(\frac12,1)$.

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English version:
Journal of Mathematical Sciences (New York), 2013, 193:1, 136–144

Bibliographic databases:

UDC: 511.466+517.863
Received: 30.08.2012

Citation: O. M. Fomenko, “Extreme values of automorphic $L$-functions”, Analytical theory of numbers and theory of functions. Part 27, Zap. Nauchn. Sem. POMI, 404, POMI, St. Petersburg, 2012, 233–247; J. Math. Sci. (N. Y.), 193:1 (2013), 136–144

Citation in format AMSBIB
\Bibitem{Fom12}
\by O.~M.~Fomenko
\paper Extreme values of automorphic $L$-functions
\inbook Analytical theory of numbers and theory of functions. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 404
\pages 233--247
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5271}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3029604}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 193
\issue 1
\pages 136--144
\crossref{https://doi.org/10.1007/s10958-013-1442-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884980698}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. M. Fomenko, “On the Dedekind zeta function. II”, J. Math. Sci. (N. Y.), 207:6 (2015), 923–933  mathnet  crossref
    2. O. M. Fomenko, “Extreme values of Epstein zeta-functions”, J. Math. Sci. (N. Y.), 222:5 (2017), 690–702  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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