Graphical cyclic supercharacters for composite moduli
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Abstract:
Recent work has introduced the study of graphical properties of cyclic supercharacters, functions $\mathbb {Z}/n\mathbb {Z}\to \mathbb {C}$ whose values are exponential sums with close connections to Gauss sums and Gaussian periods. Plots of these functions exhibit striking features, some of which have been previously explained when the modulus $n$ is a power of an odd prime. After reviewing this material, we initiate the graphical study of images of cyclic supercharacters in the case of composite $n$.References
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Additional Information
- Bob Lutz
- Affiliation: Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, Michigan 48109
- MR Author ID: 1053423
- Email: boblutz@umich.edu
- Received by editor(s): January 8, 2016
- Received by editor(s) in revised form: January 12, 2016
- Published electronically: May 17, 2019
- Communicated by: Ken Ono
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3649-3663
- MSC (2010): Primary 11L03; Secondary 11L05, 11T24
- DOI: https://doi.org/10.1090/proc/13094
- MathSciNet review: 3993760