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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Large character sums
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by Andrew Granville and K. Soundararajan PDF
J. Amer. Math. Soc. 14 (2001), 365-397 Request permission


We make conjectures and give estimates for how large character sums can be as we vary over all characters mod $q$, and as we vary over real, quadratic characters. In particular we show that the largest sums seem to depend on the value of the character at “smooth numbers”.
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Additional Information
  • Andrew Granville
  • Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
  • MR Author ID: 76180
  • ORCID: 0000-0001-8088-1247
  • Email:
  • K. Soundararajan
  • Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
  • Address at time of publication: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
  • MR Author ID: 319775
  • Email:,
  • Received by editor(s): March 29, 1999
  • Received by editor(s) in revised form: September 8, 2000
  • Published electronically: October 20, 2000
  • Additional Notes: The first author is a Presidential Faculty Fellow. He is also supported, in part, by the National Science Foundation. The second author is partially supported by the American Institute of Mathematics (AIM)

  • Dedicated: Dedicated to John Friedlander
  • © Copyright 2000 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 14 (2001), 365-397
  • MSC (2000): Primary 11L40; Secondary 11N25
  • DOI:
  • MathSciNet review: 1815216