The Uniformity Conjecture in Additive Combinatorics
Ilya D. Shkredov, Jozsef Solymosi
TL;DR
This paper explores the implications of the Bombieri-Lang conjecture in additive combinatorics, providing bounds on sumsets of powers and the sum-product problem for matchings, advancing understanding of these mathematical structures.
Contribution
It introduces new bounds on sumsets of squares and higher powers, applying the Bombieri-Lang conjecture to additive combinatorics problems.
Findings
Bounds on sumsets of squares and higher powers
Bounds on the sum-product problem for matchings
Application of the Bombieri-Lang conjecture in additive combinatorics
Abstract
In this paper we show examples for applications of the Bombieri-Lang conjecture in additive combinatorics, giving bounds on the cardinality of sumsets of squares and higher powers of integers. Using similar methods we give bounds on the sum-product problem for matchings.
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