A note on additive twists, reciprocity laws and quantum modular forms
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We prove that the central values of additive twists of a cuspidal L-function define a quantum modular form in the sense of Zagier, generalizing recent results of Bettin and Drappeau. From this, we deduce a reciprocity law for the twisted first moment of multiplicative twists of cuspidal L-functions, similar to reciprocity laws discovered by Conrey for the twisted second moment of Dirichlet L-functions. Furthermore, we give an interpretation of quantum modularity at infinity for additive twists of L-functions of weight 2 cusp forms in terms of the corresponding functional equations.
Originalsprog | Engelsk |
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Tidsskrift | Ramanujan Journal |
Vol/bind | 56 |
Sider (fra-til) | 151–162 |
ISSN | 1382-4090 |
DOI | |
Status | Udgivet - 2021 |
ID: 249254674