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.
Original language | English |
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Journal | Ramanujan Journal |
Volume | 56 |
Pages (from-to) | 151–162 |
ISSN | 1382-4090 |
DOIs | |
Publication status | Published - 2021 |
- Additive twists, Holomorphic cusp forms, Quantum modular forms, Reciprocity laws
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