Large character sums

Authors:
Andrew Granville and K. Soundararajan

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

Published electronically:
October 20, 2000

MathSciNet review:
1815216

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We make conjectures and give estimates for how large character sums can be as we vary over all characters mod , 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

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

Email:
skannan@math.princeton.edu, ksound@ias.edu

DOI:
https://doi.org/10.1090/S0894-0347-00-00357-X

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

Article copyright:
© Copyright 2000
American Mathematical Society