# 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} }

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…

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