• Corpus ID: 119624830

# Central values of additive twists of modular $L$-functions

@article{Nordentoft2018CentralVO,
title={Central values of additive twists of modular \$L\$-functions},
author={Asbj{\o}rn Christian Nordentoft},
journal={arXiv: Number Theory},
year={2018}
}
• A. Nordentoft
• Published 20 December 2018
• Mathematics
• arXiv: Number Theory
Additive twists of a modular $L$-function are important invariants associated to a cusp form, since the additive twists encode the Eichler-Shimura isomorphism. In this paper we prove that additive twists of $L$-functions associated to cusp forms $f$ of even weight are asymptotically normally distributed. This generalizes a recent breakthrough of Petridis and Risager concerning the arithmetic distribution of modular symbols. Furthermore we present applications to the moments of $L(f\otimes \chi… Wide moments of$L$-functions I: Twists by class group characters of imaginary quadratic fields We calculate certain "wide moments" of central values of Rankin--Selberg$L$-functions$L(\pi\otimes \Omega, 1/2)$where$\pi$is a cuspidal automorphic representation of$\mathrm{GL}_2$over Dynamics of continued fractions and distribution of modular symbols • Mathematics • 2019 We formulate a thermodynamical approach to the study of distribution of modular symbols, motivated by the work of Baladi-Vallee. 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Fourier coefficients of the resolvent for a Fuchsian group.
*~T + ~T~2~)~2ifc.y-r— acting on a Hubert space §k of automorphic forms dx dy) dx of weight k e IR. In this paper, we present the basic eigenfunction expansions of Gs k(z, z') and discuss
Topics in classical automorphic forms
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FUNCTORIALITY FOR THE EXTERIOR SQUARE OF GL4 AND THE SYMMETRIC FOURTH OF GL2
• Mathematics
• 2003
Let ∧ : GLn(C) −→ GLN (C), where N = n(n−1) 2 , be the map given by the exterior square. Then Langlands’ functoriality predicts that there is a map from cuspidal representations of GLn to automorphic