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Talk: Interpolated sequences and critical L-values of modular forms (Gainesville)

Interpolated sequences and critical L-values of modular forms (Gainesville)

Date: 2019/11/03
Occasion: AMS Fall Southeastern Sectional Meeting, Special Session on Partition Theory and Related Topics
Place: University of Florida

Abstract

It is well-known that the Apéry numbers which arise in the irrationality proof for \(\zeta(3)\) satisfy many interesting arithmetic properties and are related to the Fourier coefficients of a weight 4 modular form. Recently, Zagier expressed an interpolated version of these numbers in terms of a critical \(L\)-value of the same modular form. We discuss this evaluation as well as extensions, including to interpolations of Zagier's six sporadic sequences and the sequences associated to Brown's cellular integrals.

This talk is based on joint work with Robert Osburn.

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