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The graphic nature of Gaussian periods


Authors: William Duke, Stephan Ramon Garcia and Bob Lutz
Journal: Proc. Amer. Math. Soc. 143 (2015), 1849-1863
MSC (2010): Primary 11L05, 11L99, 11T22, 11T23, 11T24
DOI: https://doi.org/10.1090/S0002-9939-2015-12322-2
Published electronically: January 8, 2015
MathSciNet review: 3314096
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Abstract | References | Similar Articles | Additional Information

Abstract: Recent work has shown that the study of supercharacters on
abelian groups provides a natural framework within which to study certain exponential sums of interest in number theory. Our aim here is to initiate the study of Gaussian periods from this novel perspective. Among other things, our approach reveals that these classical objects display dazzling visual patterns of great complexity and remarkable subtlety.


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Additional Information

William Duke
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-1555
Email: wdduke@ucla.edu

Stephan Ramon Garcia
Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711
Email: Stephan.Garcia@pomona.edu

Bob Lutz
Affiliation: Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, Michigan 48109-1043
Email: boblutz@umich.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12322-2
Received by editor(s): July 26, 2013
Published electronically: January 8, 2015
Additional Notes: The first author was partially supported by National Science Foundation Grants DMS-10-01527, DMS-1001614, and DMS-1265973.
Communicated by: Ken Ono
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.