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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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Volume 30, Issue 4

Issues

Equivariant Gauss sum of finite quadratic forms

Shouhei Ma
Published Online: 2018-01-11 | DOI: https://doi.org/10.1515/forum-2017-0070

Abstract

The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum twisted by the action of the orthogonal group. We prove that simple arithmetic formulas hold for some basic classes of quadratic forms. In applications, such invariant appears in the dimension formula for certain vector-valued modular forms.

Keywords: Gauss sum; finite quadratic forms; finite orthogonal groups; Weil representation

MSC 2010: 11L05; 11E99; 11F27

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About the article


Received: 2017-04-01

Revised: 2017-11-17

Published Online: 2018-01-11

Published in Print: 2018-07-01


Citation Information: Forum Mathematicum, Volume 30, Issue 4, Pages 1029–1047, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0070.

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