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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Quantitative structure of stable sets in finite abelian groups
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by C. Terry and J. Wolf PDF
Trans. Amer. Math. Soc. 373 (2020), 3885-3903

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
  • © Copyright 2020 by the authors
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 3885-3903
  • MSC (2010): Primary 11B30
  • DOI: https://doi.org/10.1090/tran/8056
  • MathSciNet review: 4105513