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

Access to Document

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

Cite this

@article{1ec2a8312052405b931a521d69b36ccd,

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.",

author = "F. Beukers",

year = "1985",

month = oct,

doi = "10.1016/0022-314X(85)90047-2",

language = "English",

volume = "21",

pages = "141--155",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Some congruences for the Apery numbers

AU - Beukers, F.

PY - 1985/10

Y1 - 1985/10

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0002039277&partnerID=8YFLogxK

U2 - 10.1016/0022-314X(85)90047-2

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

M3 - Article

AN - SCOPUS:0002039277

SN - 0022-314X

VL - 21

SP - 141

EP - 155

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 2

ER -

Some congruences for the Apery numbers

Abstract

Access to Document

Fingerprint

Cite this