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2020 Discretized sum-product for large sets
Changhao Chen
Mosc. J. Comb. Number Theory 9(1): 17-27 (2020). DOI: 10.2140/moscow.2020.9.17

Abstract

Let A [ 1 , 2 ] be a ( δ , σ ) -set with measure | A | = δ 1 σ in the sense of Katz and Tao. For σ ( 1 2 , 1 ) we show that

| A + A | + | A A | δ c | A |

for c = ( 1 σ ) ( 2 σ 1 ) ( 6 σ + 4 ) . This improves the bound of Guth, Katz, and Zahl for large σ .

Citation

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Changhao Chen. "Discretized sum-product for large sets." Mosc. J. Comb. Number Theory 9 (1) 17 - 27, 2020. https://doi.org/10.2140/moscow.2020.9.17

Information

Received: 17 June 2019; Revised: 3 October 2019; Accepted: 28 October 2019; Published: 2020
First available in Project Euclid: 20 March 2020

zbMATH: 07171952
MathSciNet: MR4066556
Digital Object Identifier: 10.2140/moscow.2020.9.17

Subjects:
Primary: 05B99

Rights: Copyright © 2020 Mathematical Sciences Publishers

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