Congruences for Apéry numbers βn =∑k=0nn k2n+k k-Reference-Cited by-同舟云学术

Congruences for Apéry numbers βn =∑k=0nn k2n+k k

Published:2019-12-18 Issue:05 Volume:16 Page:981-1003
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Cao Hui-Qin¹,Matiyasevich Yuri²,Sun Zhi-Wei³

Affiliation:

1. Department of Applied Mathematics, Nanjing Audit University, Nanjing 211815, P. R. China

2. St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Fontanka 27, 191023, St. Petersburg, Russia

3. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

Abstract

In this paper, we establish some congruences involving the Apéry numbers [Formula: see text]. For example, we show that [Formula: see text] for any positive integer [Formula: see text], and [Formula: see text] for any prime [Formula: see text], where [Formula: see text] is the [Formula: see text]th Bernoulli number. We also present certain relations between congruence properties of the two kinds of Aṕery numbers, [Formula: see text] and [Formula: see text].

Funder

NSFC

RFBR

Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042120500505

Reference20 articles.

1. Proof of some conjectures of Z.-W. Sun on congruences for Apéry polynomials

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1. The asymptotic log-convexity of Apéry-like numbers;Journal of Difference Equations and Applications;2023-08-03

2. Two congruences concerning Apéry numbers conjectured by Z.-W. Sun;Electronic Research Archive;2020