The graphic nature of Gaussian periods
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- by William Duke, Stephan Ramon Garcia and Bob Lutz PDF
- Proc. Amer. Math. Soc. 143 (2015), 1849-1863 Request permission
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.References
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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
- MR Author ID: 726101
- 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
- MR Author ID: 1053423
- Email: boblutz@umich.edu
- 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
- © Copyright 2015
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3314096