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arXiv · 1806.05207

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

Robert Osburn·Armin Straub
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Abstract

Recently, Zagier expressed an interpolated version of the Ap\'ery 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.

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Robert Osburn, Armin Straub. 2018-06-13. Interpolated sequences and critical $L$-values of modular forms. https://doi.org/10.1007/978-3-030-04480-0_14

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