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Speaker:

Wadim Zudilin
Affiliation:

U. Newcastle (Australia) / Radboud Universiteit Nijmegen
Date:

Wed, 2016-12-14 14:15 - 15:15
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar I will examine instances of modularity of (rigid) Calabi--Yau manifolds whose periods are expressed in terms of hypergeometric functions. The $p$-th coefficients $a(p)$ of the corresponding modular form can be often read off, at least conjecturally, from the truncated partial sums of the underlying hypergeometric series modulo a power of $p$ and from Weil's general bounds $|a(p)|\le2p^{(m-1)/2}$, where $m$ is the weight of the form. Furthermore, the critical $L$-values of the modular form are predicted to be rationally proportional to the values of a related basis of solutions to the hypergeometric differential equation.

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