Geodesic
Behavior of the $L$-functions of cusp forms at~$s=1$
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 11, Tome 204 (1993), pp. 37-54

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Let $f(z)$ be a Hecke eigenform in the space $S_{2k}(\Gamma)$ of holomorphic $\Gamma$-cusp forms of even weight $2k$, $\Gamma=\mathrm{SL}(2,\mathbb Z)$; let $L_f(s)$ be the $L$-function of $f(z)$. The goal of this paper is to obtain some results on $L_f(1)$ as $k$ increases. In particular, we prove an analogue of the classical Landau theorem in the theory of Dirichlet $L$-functions and (under a very plausible hypothesis) an analogue of the famous Siegel theorem. Bibliography: 15 titles. 
@article{ZNSL_1993_204_a2,
     author = {E. P. Golubeva and O. M. Fomenko},
     title = {Behavior of the $L$-functions of cusp forms at~$s=1$},
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     pages = {37--54},
     publisher = {mathdoc},
     volume = {204},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1993_204_a2/}
}
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E. P. Golubeva; O. M. Fomenko. Behavior of the $L$-functions of cusp forms at~$s=1$. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 11, Tome 204 (1993), pp. 37-54. http://geodesic.mathdoc.fr/item/ZNSL_1993_204_a2/