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arXiv · 1402.6509

A family of mock theta functions of weights 1/2 and 3/2 and their congruence properties

René Olivetto
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Abstract

In a private communication, K. Ono conjectured that any mock theta function of weight 1/2 or 3/2 can be congruent modulo a prime $p$ to a weakly holomorphic modular form for just a few values of $p$. In this paper we describe when such a congruence occurs. More precisely we show that it depends on the $p$-adic valuation of the mock theta function itself. In order to do so, we construct a family of mock theta functions in terms of derivatives of the Appell sum, which have a special Fourier expansion at infinity.

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René Olivetto. 2014-02-26. A family of mock theta functions of weights 1/2 and 3/2 and their congruence properties. https://arxiv.org/abs/1402.6509

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