Geodesic
Extreme values of automorphic $L$-functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 233-247
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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 $\sigma_0\in\big(\frac12,1\big)$. 
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O. M. Fomenko. Extreme values of automorphic $L$-functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 233-247. http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a14/

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