Moments of mixed Kloosterman sums, supercharacters, and elliptic curves

DOI10.1007/s11139-023-00740-2OpenAlexW4380624374MaRDI QIDQ6073932

Gautam Kalita, Fahim Sayed

Publication date: 18 September 2023

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-023-00740-2

zbMATH Keywords

elliptic curvessupercharacter theorymixed Kloosterman sum

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Exponential sums (11T23) Gauss and Kloosterman sums; generalizations (11L05) Representation theory of groups (20C99)

Cites Work

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• Supercharacters, exponential sums, and the uncertainty principle.
• Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs
• The cyclotomy of finite commutative P.I.R.'s
• Motivic orthogonal two-dimensional representations of \(\text{Gal}(\overline\mathbb{Q}/\mathbb{Q})\)
• Ramanujan sums as supercharacters
• Supercharacters, elliptic curves, and the sixth moment of Kloosterman sums
• Eighth power moment of Kloosterman sum, supercharacters, and elliptic curves
• The modularity of the Barth--Nieto quintic and its relatives
• Supercharacters and mixed moments of Kloosterman sums
• Galois representations attached to moments of Kloosterman sums and conjectures of Evans
• Hypergeometric $\mathbf {{}_3{\it F}_2(1/4)}$ evaluations over finite fields and Hecke eigenforms
• Supercharacters and superclasses for algebra groups
• The cyclotomy of Kloosterman sums
• The basic character table of the unitriangular group
• Seventh power moments of Kloosterman sums
• Moments of Kloosterman sums, supercharacters, and elliptic curves

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