Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Identities on quadratic Gauss sums

Authors: Paul Gérardin and Wen-Ch’ing Winnie Li
Journal: Trans. Amer. Math. Soc. 321 (1990), 159-182
MSC: Primary 11S37; Secondary 11L05, 22E50
MathSciNet review: 974516
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Abstract: Given a local field $ F$, each multiplicative character $ \theta $ of the split algebra $ F \times F$ or of a separable quadratic extension of $ F$ has an associated generalized Gauss sum $ \gamma _\theta ^F$. It is a complex valued function on the character group of $ {F^ \times } \times F$, meromorphic in the first variable. We define a pairing between such Gauss sums and study its properties when $ F$ is a nonarchimedean local field. This has important applications to the representation theory of $ GL(2,F)$ and correspondences $ [{\text{GL}}3]$.

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Keywords: Gauss sum, quadratic gamma factor
Article copyright: © Copyright 1990 American Mathematical Society