On periodic \(\text{mod }p\) sequences and \(G\)-functions. (On a conjecture of Ruzsa)
type: Item
instance of: scholarly article
title: On periodic \(\text{mod }p\) sequences and \(G\)-functions. (On a conjecture of Ruzsa)
zbMATH Open document ID: 0864.11005
DOI: 10.1007/BF02568314
author: Umberto Zannier
published in: Manuscripta Mathematica
publication date: 1997-01-14T00:00:00Z
full work available at URL: https://eudml.org/doc/156201
review text: Let the function \(f:\mathbb{N} \to\mathbb{Z}\) satisfy (i) \(f(n+b) \equiv f(n) \bmod b\) for all natural \(b,n\); (ii) \(f(n)= O(e^{\alpha n})\) where \(\alpha<1\). Then I. Z. Ruzsa conjectured that \(f\) is a polynomial. He provided this with \(e-1\) instead of \(e\) in (ii). In this paper the author proves it with \(\exp (0,75) \approx 2,1\) and (i) for all large primes \(p\) instead of \(b\). He uses the arithmetic theory of \(G\)-functions.
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 952698
zbMATH Keywords: periodic mod \(p\) sequences
zbMATH Keywords: conjecture of Ruzsa
zbMATH Keywords: \(G\)-functions
Wikidata QID: Q123246781
reviewed by: Jürgen Spilker
MaRDI profile type: Publication
cites work: Q3679314
cites work: An Introduction to "G"-Functions. (AM-133)
cites work: On pseudo‐polynomials
cites work: Q3665180
cites work: A note on recurrent mod p sequences
OpenAlex ID: W2910495728
description: scientific article; zbMATH DE number 952698