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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 404, Pages 233–247
(Mi znsl5271)
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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,
$$
\log\Bigg|L\Biggl(\frac12+it,f\times f\Biggr)\Bigg|=\Omega_+\Biggl(\Biggl(\frac{\log t}{\log\log t}\Biggr)^{1/2}\Biggr),
$$
and
$$
\log\big|L(\sigma_0+it,f\times f)\big|=\Omega_+\Biggl(\Biggl(\frac{\log t}{\log\log t}\Biggr)^{1-\sigma_0}\Biggr)
$$
for fixed $\sigma_0\in\big(\frac12,1\big)$.
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
Linking options:
https://www.mathnet.ru/eng/znsl5271 https://www.mathnet.ru/eng/znsl/v404/p233
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Abstract page: | 263 | Full-text PDF : | 48 | References: | 41 |
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