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Sums of multiplicative characters with additive convolutions

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Abstract

We obtain new estimates for binary and ternary sums of multiplicative characters with additive convolutions of characteristic functions of sets with small additive doubling. In particular, we improve a result of Mei-Chu Chang. The proof uses the Croot–Sisask almost periodicity lemma.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    A. S. Volostnov & I. D. Shkredov

Authors
  1. A. S. Volostnov
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  2. I. D. Shkredov
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Correspondence to A. S. Volostnov.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 296, pp. 265–279.

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Volostnov, A.S., Shkredov, I.D. Sums of multiplicative characters with additive convolutions. Proc. Steklov Inst. Math. 296, 256–269 (2017). https://doi.org/10.1134/S0081543817010217

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  • DOI: https://doi.org/10.1134/S0081543817010217

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