## Large character sums

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

## Abstract:

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”.## References

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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: andrew@math.uga.edu
**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: skannan@math.princeton.edu, ksound@ias.edu
- 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)
- © Copyright 2000 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**14**(2001), 365-397 - MSC (2000): Primary 11L40; Secondary 11N25
- DOI: https://doi.org/10.1090/S0894-0347-00-00357-X
- MathSciNet review: 1815216

Dedicated: Dedicated to John Friedlander