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2019 On products of shifts in arbitrary fields
Audie Warren
Mosc. J. Comb. Number Theory 8(3): 247-261 (2019). DOI: 10.2140/moscow.2019.8.247

Abstract

We adapt the approach of Rudnev, Shakan, and Shkredov (2018) to prove that in an arbitrary field F, for all AF finite with |A|<p14 if p:= Char(F) is positive, we have

| A ( A + 1 ) | | A | 1 1 9 ( log | A | ) 7 6 , | A A | + | ( A + 1 ) ( A + 1 ) | | A | 1 1 9 ( log | A | ) 7 6 .

This improves upon the exponent of 65 given by an incidence theorem of Stevens and de Zeeuw.

Citation

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Audie Warren. "On products of shifts in arbitrary fields." Mosc. J. Comb. Number Theory 8 (3) 247 - 261, 2019. https://doi.org/10.2140/moscow.2019.8.247

Information

Received: 6 December 2018; Revised: 30 April 2019; Accepted: 14 May 2019; Published: 2019
First available in Project Euclid: 13 August 2019

zbMATH: 07095943
MathSciNet: MR3990807
Digital Object Identifier: 10.2140/moscow.2019.8.247

Subjects:
Primary: 11B75, 68R05

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.8 • No. 3 • 2019
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