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Interpolated sequences and critical L-values of modular forms

Interpolated sequences and critical L-values of modular forms
Robert Osburn, Armin Straub — Chapter 14 of the book: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory (Springer) — Editors: J. Blümlein, P. Paule, and C. Schneider — 2019, Pages 327-349

Abstract

Recently, Zagier expressed an interpolated version of the Apéry numbers for $$\zeta(3)$$ in terms of a critical $$L$$-value of a modular form of weight 4. We extend this evaluation in two directions. We first prove that interpolations of Zagier's six sporadic sequences are essentially critical $$L$$-values of modular forms of weight 3. We then establish an infinite family of evaluations between interpolations of leading coefficients of Brown's cellular integrals and critical $$L$$-values of modular forms of odd weight.

title = {Interpolated sequences and critical {$L$}-values of modular forms},