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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

   
 
 

 

Quantitative structure of stable sets in finite abelian groups


Authors: C. Terry and J. Wolf
Journal: Trans. Amer. Math. Soc. 373 (2020), 3885-3903
MSC (2010): Primary 11B30
DOI: https://doi.org/10.1090/tran/8056
Published electronically: March 3, 2020
MathSciNet review: 4105513
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove an arithmetic regularity lemma for stable subsets of finite abelian groups, generalising our previous result for high-dimensional vector spaces over finite fields of prime order. A qualitative version of this generalisation was recently obtained by the first author in joint work with Conant and Pillay, using model-theoretic techniques. In contrast, the approach in the present paper is highly quantitative and relies on several key ingredients from arithmetic combinatorics.


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Additional Information

C. Terry
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
MR Author ID: 1130819
Email: caterry@math.uchicago.edu

J. Wolf
Affiliation: Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
MR Author ID: 850181
Email: julia.wolf@dpmms.cam.ac.uk

Received by editor(s): June 26, 2018
Received by editor(s) in revised form: February 17, 2019
Published electronically: March 3, 2020
Article copyright: © Copyright 2020 by the authors