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Hodge structure and motivic gamma function associated to the Apéry family

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Spencer Bloch
University of Chicago / MPIM Bonn
Mon, 2018-03-12 11:00 - 12:00
MPIM Lecture Hall

(Joint work with M. Vlasenko) Inspired by recent work of V. Golyshev and D. Zagier, we associate to the  Apéry family (a rank 3 variation of Hodge structure on an open set in the projective line) a "motivic Gamma function" which is a Mellin transform of a suitable Picard Fuchs solution. The Taylor series at $s=0$ of this  Mellin transform has coefficients which numerical calculations suggest are (multiple) zeta values. We show how this data can be interpreted as a variation of mixed Hodge structure.

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