Student Co-author

Pomona Undergraduate

Document Type

Article - preprint


Mathematics (Pomona)

Publication Date



Kloosterman sum, Gauss sum, Salie sum, supercharacter, hypocycloid, uniform distribution, equidistribution, Lucas number, Lucas prime


For a positive integer m and a subgroup A of the unit group (Z/mZ)x, the corresponding generalized Kloosterman sum is the function K(a, b, m, A) = ΣuEA e(au+bu-1/m). Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features when their values are plotted in the complex plane. In a variety of instances, we identify the precise number-theoretic conditions that give rise to particular phenomena.


Final published version can be found at: Burkhardt, P., Chan, A. Z.-Y., Currier, G., Garcia, S.R., Luca, F., Suh, H., Visual properties of generalized Kloosterman sums, Journal of Number Theory 160 (2016), 237-253.

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© 2015 Elsevier Inc.

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Number Theory Commons