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Journal of the American Mathematical Society

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Large character sums

Authors: Andrew Granville and K. Soundararajan
Journal: J. Amer. Math. Soc. 14 (2001), 365-397
MSC (2000): Primary 11L40; Secondary 11N25
Published electronically: October 20, 2000
MathSciNet review: 1815216
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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''.

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Additional Information

Andrew Granville
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602

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

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