A converse theorem in half-integral weight

Steven Creech; Henry Twiss

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arXiv · 2306.02872

A converse theorem in half-integral weight

Steven Creech·Henry Twiss

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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.

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Steven Creech, Henry Twiss. 2023-06-05. A converse theorem in half-integral weight. https://arxiv.org/abs/2306.02872

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