Geodesic
The distribution of the values of Hecke $L$-functions at 1
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 15-32 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $S_2(q)$ be the set of primitive forms in the space $S_2(\Gamma_0(q))$ of holomorpic $\Gamma_0(q)$-cusp forms of weight $2$. Let $f\in S_2(q)$ and let $L_f(S)$ be the $L$-function of $f(z)$. It is proved that the set $\{\log L_f(1) has a limit distribution function. The rate of convergence to this limit function is estimated. 
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E. P. Golubeva. The distribution of the values of Hecke $L$-functions at 1. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 20, Tome 314 (2004), pp. 15-32. http://geodesic.mathdoc.fr/item/ZNSL_2004_314_a1/

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