ACAC Seminar Abstract

ACAC Seminar Abstract

ACAC Seminars

ACAC Seminar Abstract

Linear multivariate forms in combinatorial number theory

Speaker: Juanjo Rué
Date, Time: Fri, 17 Aug 2012 14:30

Let A be a set of non-negative integers. Several questions concerning additive properties of A are related to properties of the set {a +a': a,a' in A}. However, many other interesting questions appear when we consider the set {ka+ja' : a,a' in A}, where k and j are positive integers. In this talk, we expose two topics related to this framework. When A is an infinite set, we study the number of solutions of the equation n=ka+ja', with a and a' in A and. We prove that this function, in terms of n, is not constant for n large enough. This partially solves a problem posted by Sárközy and Sós. We also show Erdós-Fuchs type results in several cases. When A is a finite set, we study the size of the set {ka+ja': a,a' in A} in terms of the size of A. Our results here provide explicit constructions which are tight in some cases.
These results are based on joint works with Javier Cilleruelo (first part) and Yahya Ould Hamidoune (second part).

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