Attaining the Exponent 5/4 for the Sum-Product Problem in Finite Fields-Reference-Cited by-同舟云学术

Attaining the Exponent 5/4 for the Sum-Product Problem in Finite Fields

Published:2021-12-15 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Mohammadi Ali¹,Stevens Sophie²

Affiliation:

1. School of Mathematics, Institute for Research in Fundamental Sciences, 19395-5746 Tehran, Iran

2. Johannn Radon Institute for Computational and Applied Mathematics, 4040 Linz, Austria

Abstract

Abstract We improve the exponent in the finite field sum-product problem from $11/9$ to $5/4$, improving the results of Rudnev et al. [16]. That is, we show that if $A\subset \mathbb {F}_p$ has cardinality $|A|\ll p^{1/2}$, then $ \max \{|A\pm A|,|AA|\} \gtrsim |A|^\frac 54 $ and $ \max \{|A\pm A|,|A/A|\}\gtrsim |A|^\frac 54 $.

Funder

Austrian Science Fund FWF grants

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnab338/41779585/rnab338.pdf

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