Moments of Kloosterman sums, supercharacters, and elliptic curves

Fahim Sayed and Gautam Kalita
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Fahim Sayed: Department of Science and Mathematics, Indian Institute of Information Technology Guwahati
Gautam Kalita: Department of Science and Mathematics, Indian Institute of Information Technology Guwahati

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 1, 200-209

Abstract: Abstract In this paper, we use a supercharacter theory for $${\mathbb {F}}_p^2$$ F p 2 induced by the action of a subgroup of GL $$_2({\mathbb {F}}_p)$$ 2 ( F p ) to express the fifth and seventh power moments of Kloosterman sums in terms of traces of Frobenius endomorphism for certain families of elliptic curves.

Keywords: Kloosterman sum; Supercharacter theory; Elliptic curves; 11L05; 20C99; 11G20; 11T23 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00243-8

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