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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Imprimitive Gaussian sums and theta functions over a number field
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by Jacob Nemchenok PDF
Trans. Amer. Math. Soc. 338 (1993), 465-478 Request permission

Abstract:

We obtain a reduction formula for an imprimitive Gaussian sum with a numerical character in an algebraic number field, i.e. a formula that expresses that sum as a product of several elementary factors times a primitive, proper, normed Gaussian sum (formulae (16) and (19)). We also introduce Gaussian sums with Hecke characters and derive a similar reduction formula for them. The derivation is based on an inversion formula for a multivariable theta function associated with the number field, twisted with the numerical character.
References
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 338 (1993), 465-478
  • MSC: Primary 11L05; Secondary 11F11, 11F12
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1041052-9
  • MathSciNet review: 1041052