TY - JOUR

T1 - Additive correlation and the inverse problem for the large sieve

AU - Hanson, Brandon

N1 - Publisher Copyright:
Copyright © Cambridge Philosophical Society 2018.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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.

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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U2 - 10.1017/S0305004118000518

DO - 10.1017/S0305004118000518

M3 - Article

AN - SCOPUS:85049616675

VL - 168

SP - 211

EP - 217

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 2

ER -