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- W2949858172 abstract "Let $f$ be a primitive cusp form of weight $k$ and level $N,$ let $chi$ be a Dirichlet character of conductor coprime with $N,$ and let $mathfrak{L}(fotimes chi, s)$ denote either $log L(fotimes chi, s)$ or $(L'/L)(fotimes chi, s).$ In this article we study the distribution of the values of $mathfrak{L}$ when either $chi$ or $f$ vary. First, for a quasi-character $psicolon mathbb{C} to mathbb{C}^times$ we find the limit for the average $mathrm{Avg}_chi psi(L(fotimeschi, s)),$ when $f$ is fixed and $chi$ varies through the set of characters with prime conductor that tends to infinity. Second, we prove an equidistribution result for the values of $mathfrak{L}(fotimes chi,s)$ by establishing analytic properties of the above limit function. Third, we study the limit of the harmonic average $mathrm{Avg}^h_f psi(L(f, s)),$ when $f$ runs through the set of primitive cusp forms of given weight $k$ and level $Nto infty.$ Most of the results are obtained conditionally on the Generalized Riemann Hypothesis for $L(fotimeschi, s).$" @default.
- W2949858172 created "2019-06-27" @default.
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- W2949858172 date "2016-12-31" @default.
- W2949858172 modified "2023-10-18" @default.
- W2949858172 title "On M-functions associated with modular forms" @default.
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