Additive correlation and the inverse problem for the large sieve

Brandon Hanson

doi:10.1017/S0305004118000518

Additive correlation and the inverse problem for the large sieve

Brandon Hanson

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let A [1, N] be a set of integers with |A| ≫. We show that if A avoids about p/2 residue classes modulo p for each prime p, then A must correlate additively with the squares S = {n² : 1 ≤ n ≤ }, in the sense that we have the additive energy estimate This is, in a sense, optimal.

Original language	English (US)
Pages (from-to)	211-217
Number of pages	7
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	168
Issue number	2
DOIs	https://doi.org/10.1017/S0305004118000518
State	Published - Mar 1 2020

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1017/S0305004118000518

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abstract = "Let A [1, N] be a set of integers with |A| ≫. We show that if A avoids about p/2 residue classes modulo p for each prime p, then A must correlate additively with the squares S = \{n2 : 1 ≤ n ≤ \}, in the sense that we have the additive energy estimate This is, in a sense, optimal.",

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AB - Let A [1, N] be a set of integers with |A| ≫. We show that if A avoids about p/2 residue classes modulo p for each prime p, then A must correlate additively with the squares S = {n2 : 1 ≤ n ≤ }, in the sense that we have the additive energy estimate This is, in a sense, optimal.

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Additive correlation and the inverse problem for the large sieve

Abstract

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