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