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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Large even order character sums


Authors: Leo Goldmakher and Youness Lamzouri
Journal: Proc. Amer. Math. Soc. 142 (2014), 2609-2614
MSC (2010): Primary 11L40
Published electronically: April 8, 2014
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Abstract: A classical theorem of Paley asserts the existence of an infinite family of quadratic characters whose character sums become exceptionally large. In this paper, we establish an analogous result for characters of any fixed even order. Previously our bounds were only known under the assumption of the Generalized Riemann Hypothesis.


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Additional Information

Leo Goldmakher
Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
Email: lgoldmak@math.toronto.edu

Youness Lamzouri
Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada
Email: lamzouri@mathstat.yorku.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11990-3
PII: S 0002-9939(2014)11990-3
Received by editor(s): May 15, 2012
Received by editor(s) in revised form: May 17, 2012, and August 19, 2012
Published electronically: April 8, 2014
Additional Notes: The first author was partially supported by an NSERC Discovery Grant
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2014 American Mathematical Society