On the rate of p-adic convergence of sums of powers of binomial coefficients

Author:

Lengyel Tamás1ORCID

Affiliation:

1. Mathematics Department, Occidental College, Los Angeles, CA 90041, USA

Abstract

Let [Formula: see text] be an integer and [Formula: see text] be an odd prime. We study sums and lacunary sums of [Formula: see text]th powers of binomial coefficients from the point of view of arithmetic properties. We develop new congruences and prove the [Formula: see text]-adic convergence of some subsequences and that in every step we gain at least one or three more [Formula: see text]-adic digits of the limit if [Formula: see text] or [Formula: see text], respectively. These gains are exact under some explicitly given conditions. The main tools are congruential and divisibility properties of the binomial coefficients and multiple and alternating harmonic sums.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Supercongruences for some lacunary sums of powers of binomial coefficients;International Journal of Number Theory;2018-08-22

2. On some lacunary sums of even powers of binomial coefficients;International Journal of Number Theory;2017-09-20

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