A converse theorem in half-integral weight
Abstract
In this paper, we prove a converse theorem for half-integral weight modular forms assuming functional equations for $L$-series with additive twists. This result is an extension of Booker, Farmer, and Lee's result in [BFL22] to the half-integral weight setting. Similar to their work, the main result of this paper is obtained as a consequence of the half-integral weight Petersson trace formula.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2023
- DOI:
- 10.48550/arXiv.2306.02872
- arXiv:
- arXiv:2306.02872
- Bibcode:
- 2023arXiv230602872C
- Keywords:
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- Mathematics - Number Theory
- E-Print:
- 13 pages, 2 tables