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Cauchy-Davenport Theorem for abelian groups and diagonal congruences


Authors: Todd Cochrane, Misty Ostergaard and Craig Spencer
Journal: Proc. Amer. Math. Soc. 147 (2019), 3339-3345
MSC (2010): Primary 11D79, 11D72, 11P05
DOI: https://doi.org/10.1090/proc/14504
Published electronically: April 8, 2019
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Abstract: We prove an analogue of the Cauchy-Davenport Theorem and Chowla's Theorem for sum sets in a general abelian group and give an application to diagonal congruences, establishing a best possible estimate for the distribution of solutions of a diagonal congruence $ \sum _{i=1}^n a_ix_i^k \equiv c \pmod q$ with an arbitrary modulus.


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Additional Information

Todd Cochrane
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: cochrane@math.ksu.edu

Misty Ostergaard
Affiliation: Department of Mathematics, University of Southern Indiana, Evansville, Indiana 47712
Email: m.ostergaard@usi.edu

Craig Spencer
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: cvs@math.ksu.edu

DOI: https://doi.org/10.1090/proc/14504
Keywords: Cauchy-Davenport Theorem, diagonal congruences
Received by editor(s): October 27, 2017
Received by editor(s) in revised form: December 3, 2018
Published electronically: April 8, 2019
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2019 American Mathematical Society