Student Co-author

HMC Undergraduate, Pomona Undergraduate, Scripps Undergraduate, CGU Graduate

Document Type

Article - preprint

Department

Mathematics (Pomona)

Publication Date

2013

Keywords

supercharacters, classical character theory, exponential sums, uncertainty principle, Fourier transform

Abstract

The theory of supercharacters, which generalizes classical character theory, was recently introduced by P. Diaconis and I.M. Isaacs, building upon earlier work of C. Andre. We study supercharacter theories on $(Z/nZ)^d$ induced by the actions of certain matrix groups, demonstrating that a variety of exponential sums of interest in number theory (e.g., Gauss, Ramanujan, and Kloosterman sums) arise in this manner. We develop a generalization of the discrete Fourier transform, in which supercharacters play the role of the Fourier exponential basis. We provide a corresponding uncertainty principle and compute the associated constants in several cases.

Comments

Pre-print from arXiv:

Brumbaugh, J.L., Bulkow, M., Fleming, P.S., Garcia, L.A., Garcia, S.R., Karaali, G., Michal, M., Turner, A.P., Supercharacters, exponential sums, and the uncertainty principle, (submitted). http://arxiv.org/abs/1208.5271

Rights Information

© 2013 J.L. Brumbaugh, Madeleine Bulkow, Patrick S. Fleming, Luis Alberto Garcia, Stephan Ramon Garcia, Gizem Karaali, Matt Michal, Andrew P. Turner

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Download

Share

COinS