arminstraub.com

Interpolated sequences and critical L-values of modular forms

Interpolated sequences and critical L-values of modular forms
Robert Osburn, Armin Straub — Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory (Springer) — Editors: J. Blümlein, P. Paule, and C. Schneider — 2018

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.

Download

LinkSizeDescriptionHits
435.76 KB Preprint (PDF, 23 pages) 90

BibTeX

@article{zagier-apery-lvalues-2018,
    author = {Robert Osburn and Armin Straub},
    title = {Interpolated sequences and critical L-values of modular forms},
    journal = {Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory (Springer)},
    year = {2018},
}