Well distribution of Sidon sets in residue classes
type: Item
instance of: scholarly article
title: Well distribution of Sidon sets in residue classes
zbMATH Open document ID: 0912.11010
author: Bernt Lindström
published in: Journal of Number Theory
publication date: 1999-05-30T00:00:00Z
review text: Eine Menge \(A\subseteq \mathbb{N}_0\) heißt Sidon-Menge, wenn alle Summen \(a+a'\) für alle \(a\), \(a'\in A\) \((a\leq a')\) verschieden sind. Als Hauptresultat wird der folgende Satz bewiesen (Theorem 1): Sei \(A\subseteq [1,n]\) eine Sidon-Menge mit \(r:= | A| =(a+o (1))n^{1 \over 2}\). Für ein festes \(2 \leq m\in \mathbb{N}\) sei \(A_i:= \{a\in A\mid a\equiv i\pmod m\}\) und \(r_i: =| A_i |\) \((0\leq i<m)\). Dann gilt \[ \lim_{n\to\infty} {r_i\over \sqrt n} \to {1\over m}. \] Für \(m=2\) gibt Theorem 2 eine schärfere Aussage.
Mathematics Subject Classification ID: 11B83
zbMATH DE Number: 1202429
zbMATH Keywords: distribution in residue classes
zbMATH Keywords: Sidon sets
reviewed by: Erich Härtter
MaRDI profile type: Publication
full work available at URL: jnth.1997.2217
OpenAlex ID: W1996343449
cites work: Q4179025
cites work: On sums of a Sidon-sequence
cites work: On sum sets of Sidon sets. I
cites work: Q3963072
cites work: An inequality for B2-sequences
DOI: 10.1006/JNTH.1997.2217
description: scientific article; zbMATH DE number 1202429