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arXiv · 2111.08796

Ap\'ery limits for elliptic $L$-values

Christoph Koutschan·Wadim Zudilin
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Abstract

For an (irreducible) recurrence equation with coefficients from $\mathbb Z[n]$ and its two linearly independent rational solutions $u_n,v_n$, the limit of $u_n/v_n$ as $n\to\infty$, when exists, is called the Ap\'ery limit. We give a construction that realises certain quotients of $L$-values of elliptic curves as Ap\'ery limits.

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BibTeXRIS

Christoph Koutschan, Wadim Zudilin. 2021-11-16. Ap\'ery limits for elliptic $L$-values. https://doi.org/10.1017/s0004972721001295

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