Interpolated sequences and critical $L$-values of modular forms

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.

23 pages, to appear in Proceedings for the KMPB conference: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory

References in corpus (4)

• A modular supercongruence for ${}_6{F}_5$: an Apéry-like story
• A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds
• Sequences, modular forms and cellular integrals
• Mahler measure of some singular K3-surfaces

Cited by in corpus (3)

• Sequences, modular forms and cellular integrals
• Lucas congruences for the Apéry numbers modulo $p^2$
• A Whipple ${}_7{F}_6$ formula revisited