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

Christoph Koutschan; Wadim Zudilin

doi:10.1017/S0004972721001295

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

Number Theory 2022-09-09 v1 Algebraic Geometry Classical Analysis and ODEs Combinatorics

Authors: Christoph Koutschan , Wadim Zudilin

View on arXiv ↗ PDF ↗ DOI ↗

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.

Keywords

elliptic curves

Cite

@article{arxiv.2111.08796,
  title  = {Ap\'ery limits for elliptic $L$-values},
  author = {Christoph Koutschan and Wadim Zudilin},
  journal= {arXiv preprint arXiv:2111.08796},
  year   = {2022}
}

Comments

6 pages, 3 recurrence equations (including Ap\'ery's for $\zeta(3)$)

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

Abstract

Keywords

Cite

Comments

Related papers