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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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Exponential sums with multiplicative coefficients and applications
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by Régis de la Bretèche and Andrew Granville PDF
Trans. Amer. Math. Soc. 375 (2022), 6875-6901 Request permission


We show that if an exponential sum with multiplicative coefficients is large then the associated multiplicative function is “pretentious”. This leads to applications in the circle method, and a natural interpretation of the local-global principle.
Additional Information
  • Régis de la Bretèche
  • Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris Cité, Sorbonne Université, CNRS UMR 7586, Case Postale 7012, F-75251 Paris CEDEX 13, France
  • ORCID: 0000-0002-6713-9766
  • Email:
  • Andrew Granville
  • Affiliation: Départment de Mathématiques et Statistique, Université de Montréal, CP 6128 succ Centre-Ville, Montréal, Quebec H3C 3J7, Canada; and Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England.
  • MR Author ID: 76180
  • ORCID: 0000-0001-8088-1247
  • Email:
  • Received by editor(s): March 31, 2021
  • Received by editor(s) in revised form: November 12, 2021
  • Published electronically: July 25, 2022
  • Additional Notes: A.G. est partiellement soutenu par une bourse de la Conseil de recherches en sciences naturelles et en génie du Canada, and was also partially supported by a European Research Council grant, agreement n$^{\text {o}}$ 670239. Part of this work was undertaken while the second author was in Paris; his stay was supported by Université Paris–Diderot, Université Pierre et Marie Curie, Université d’Orsay and Fondation Sciences Mathématiques de Paris. The hospitality and financial support of these institutions is gratefully acknowledged.
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 6875-6901
  • DOI: