Some congruences for the Apery numbers

F. Beukers

doi:10.1016/0022-314X(85)90047-2

Some congruences for the Apery numbers

F. Beukers^*

^*Corresponding author for this work

extern

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

In 1979 R. Apéry introduced the numbers a_n = Σ₀ⁿ(_kⁿ)²(_k^{n + k}) and u_n = Σ₀ⁿ(_kⁿ)²(_k^{n + k})² in his irrationality proof for ζ(2) and ζ(3). We prove some congruences for these numbers which generalize congruences previously published in this journal.

Original language	English
Pages (from-to)	141-155
Number of pages	15
Journal	Journal of Number Theory
Volume	21
Issue number	2
DOIs	https://doi.org/10.1016/0022-314X(85)90047-2
Publication status	Published - Oct 1985
Externally published	Yes

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title = "Some congruences for the Apery numbers",

abstract = "In 1979 R. Ap{\'e}ry introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in his irrationality proof for ζ(2) and ζ(3). We prove some congruences for these numbers which generalize congruences previously published in this journal.",

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AB - In 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in his irrationality proof for ζ(2) and ζ(3). We prove some congruences for these numbers which generalize congruences previously published in this journal.

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DO - 10.1016/0022-314X(85)90047-2

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JO - Journal of Number Theory

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Some congruences for the Apery numbers

Abstract

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