Asbjorn Nordentorft (U. of Copenhagen)
Central values of additive twists of modular L-functions

Abstract: I will talk about work in preparation, in which it is shown that the central values of the “family” of additive twists of L-functions associated to a cusp form of arbitrary even weight follow a normal distribution (when appropriately normalized and ordered). Additive twists are important invariants of cusp forms, since they show up in the coefficients of the period polynomials. Recently Risager and Petridis settled a conjecture of Mazur and Rubin regarding the distribution of modular symbols. The results presented in the talk can be seen as a higher weight version of their work. In the spirit of the work of Mazur and Rubin we also present applications to the study of moments of Dirichlet twists of modular L-functions, supplementing recent work of BMMFKS. The proof has some similarities with the Shahidi-Langlands method and relies on analytic properties of resolvents.