I have a blur that whether one has $L(1,\text{sym}^2f)\ll \log^A q$ for some $A>0$? Here $f$ is assumed to be a Maass cusp form of square-free level $q$. If any experts here know something about this, please share the comments. Thanks in advance.
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1$\begingroup$ This isn't known without recourse to the Ramanujan conjecture. The best that one can do unconditionally (so far) is $L(1,\mathrm{sym}^2 f) \ll \exp(C(\log q)^{1/2} (\log \log q)^{1/4})$ for some absolute constant $C > 0$ dependent on the spectral parameter of $f$. See Corollary 1 of "Upper Bounds on $L$-Functions at the Edge of the Critical Strip" by Xiannan Li. $\endgroup$– Peter HumphriesCommented Aug 23, 2021 at 12:59
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$\begingroup$ @PeterHumphries Many thanks for your comments. Much obliged! $\endgroup$– hofnumberCommented Aug 23, 2021 at 15:44
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