Supercharacters, exponential sums, and the uncertainty principle.

DOI10.1016/j.jnt.2014.04.019zbMath1296.20004arXiv1208.5271OpenAlexW2963349591MaRDI QIDQ404337

Hong Suh, Luis Alberto Garcia German, Madeleine Bulkow, Gizem Karaali, Patrick S. Fleming, Andrew P. Turner, J. L. Brumbaugh, Stephan Ramon Garcia, Matthew Michal

Publication date: 4 September 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.5271

zbMATH Keywords

conjugacy classessymmetric groupsGauss sumsdiscrete Fourier transformuncertainty principleKloosterman sumsdiscrete cosine transformRamanujan sumssupercharactersGaussian periodsHeilbronn sumssuperclasses

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Gauss and Kloosterman sums; generalizations (11L05) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (23)

Supercharacters and the discrete Fourier, cosine, and sine transforms ⋮ Eighth power moment of Kloosterman sum, supercharacters, and elliptic curves ⋮ Supercharacters, elliptic curves, and the sixth moment of Kloosterman sums ⋮ Moments of mixed Kloosterman sums, supercharacters, and elliptic curves ⋮ Moments of Kloosterman sums, supercharacters, and elliptic curves ⋮ Restriction and induction for supercharacters of finite groups of triangular type ⋮ Visual properties of generalized Kloosterman sums ⋮ On a supercharacter analog of nilpotent groups ⋮ Lateral Movement in Undergraduate Research: Case Studies in Number Theory ⋮ A supercharacter approach to Heilbronn sums ⋮ Supercharacters and mixed moments of Kloosterman sums ⋮ Supercharacters of unipotent and solvable groups ⋮ The Graphic Nature of the Symmetric Group ⋮ Supercharacters of unipotent groups defined by involutions. ⋮ Ramanujan sums as supercharacters ⋮ The graphic nature of Gaussian periods ⋮ Unnamed Item ⋮ Supercharacter theories of type \(A\) unipotent radicals and unipotent polytopes ⋮ Supercharacter theories of type \(A\) unipotent radicals and unipotent polytopes ⋮ Supercharacter theories for Sylow \(p\)-subgroups of the Ree groups ⋮ Towards a supercharacter theory of parabolic subgroups ⋮ Graphical cyclic supercharacters for composite moduli ⋮ Ограничение и индуцирование суперхарактеров конечных групп треугольного типа

Cites Work

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• Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs
• Introduction to arithmetical functions
• The cyclotomy of finite commutative P.I.R.'s
• Trigonometric sums, Green functions of finite groups and representations of Weyl groups
• Fourier transforms on invariant functions on finite reductive Lie algebras
• An uncertainty principle for cyclic groups of prime order
• Basic characters of the unitriangular group
• Ramanujan sums as supercharacters
• Basic characters of the unitriangular group (for arbitrary primes)
• The space of invariant functions on a finite Lie algebra
• The graphic nature of Gaussian periods
• The Graphic Nature of the Symmetric Group
• Supercharacters and superclasses for algebra groups
• The basic character table of the unitriangular group

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