Journal of the
Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2010; 47(2): 409-424

Printed March 1, 2010

https://doi.org/10.4134/JKMS.2010.47.2.409

Copyright © The Korean Mathematical Society.

Identities arising from Gauss sums for symplectic and orthogonal groups

Hi-joon Chae and Dae San Kim

Hongik University and Sogang University

Abstract

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We express Gauss sums for symplectic and orthogonal groups over finite fields as averages of exponential sums over certain maximal tori. Together with our previous results, we obtain some interesting identities involving various classical Gauss and Kloosterman sums.

Keywords: Gauss sums, exponential sums, symplectic groups, orthogonal groups

MSC numbers: 55A19, 11T24, 20G40

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