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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Identities on quadratic Gauss sums
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by Paul Gérardin and Wen-Ch’ing Winnie Li PDF
Trans. Amer. Math. Soc. 321 (1990), 159-182 Request permission

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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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 321 (1990), 159-182
  • MSC: Primary 11S37; Secondary 11L05, 22E50
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0974516-1
  • MathSciNet review: 974516