Ramanujan Sums as Supercharacters

Authors

Christopher F. Fowler '12, Pomona College
Stephan Ramon Garcia, Pomona CollegeFollow
Gizem Karaali, Pomona CollegeFollow

Document Type

Article - preprint

Department

Mathematics (Pomona)

Publication Date

2012

Keywords

supercharacters, Ramanujan sums

Abstract

The theory of supercharacters, recently developed by Diaconis-Isaacs and Andre, can be used to derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently yields one-line proofs of difficult identities and provides many novel formulas. In addition to exhibiting a new application of supercharacter theory, this article also serves as a blueprint for future work since some of the abstract results we develop are applicable in much greater generality.

Comments

Pre-print from http://arxiv.org/abs/1201.1060

Final publication can be found at:

Fowler, C., Garcia, S.R., Karaali, G., Ramanujan sums as supercharacters, Ramanujan J. http://www.springer.com/mathematics/numbers/journal/11139

Rights Information

© 2013 Springer-Verlag

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Fowler, Christopher F. '12; Garcia, Stephan Ramon; and Karaali, Gizem, "Ramanujan Sums as Supercharacters" (2012). Pomona Faculty Publications and Research. 147.
https://scholarship.claremont.edu/pomona_fac_pub/147