Prime power divisors of binomial coefficients
type: Item
instance of: scholarly article
title: Prime power divisors of binomial coefficients
zbMATH Open document ID: 0952.11002
DOI: 10.1016/S0012-365X(98)00326-4
author: G. A. Kolesnik
author: P. Erdős
published in: Discrete Mathematics
publication date: 2001-01-08T00:00:00Z
review text: This excellent paper provides \textit{asymptotic} bounds for the number of primes \(p\) such that \(p^r\|\binom{n}{m}\), when \(n\) goes to infinity and \(m\) is larger than some power of \(n\). The uniformity in \(r\) is furthermore carried out. The method is deceptively simple looking and relies on a lemma (Lemma~3) of great generality that gives a Vinogradov type bound for exponential sums over primes, a lemma which is worth looking at on its own.
reviewed by: Olivier Ramaré
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 11L03
Mathematics Subject Classification ID: 11L20
zbMATH DE Number: 1334444
zbMATH Keywords: divisibility of binomial coefficients
zbMATH Keywords: exponential sums over primes
zbMATH Keywords: Vinogradov type bound
MaRDI profile type: Publication
cites work: Q4103585
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full work available at URL: s0012-365x(98)00326-4
OpenAlex ID: W2058291074
description: scientific article; zbMATH DE number 1334444