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arXiv · 1402.1116

Kummer congruences arising from the mirror symmetry of an elliptic curve

Adele Lopez
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Abstract

In the genus 1 case, mirror symmetry reduces to the statement that a certain family of generating functions, relating to an elliptic curve, are quasimodular. In their proof of this fact, Kaneko and Zagier used a related family of generating functions $A_n(\tau)$, which they show to be quasimodular. We show that these $A_n$'s also satisfy Kummer-type congruences. Additionally, we show that for a prime $p$, the $p$th power coefficients of $A_n$ $p$-adically converge to zero, for specific values of $n$.

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Adele Lopez. 2014-02-05. Kummer congruences arising from the mirror symmetry of an elliptic curve. https://arxiv.org/abs/1402.1116

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