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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Imprimitive Gaussian sums and theta functions over a number field


Author: Jacob Nemchenok
Journal: Trans. Amer. Math. Soc. 338 (1993), 465-478
MSC: Primary 11L05; Secondary 11F11, 11F12
MathSciNet review: 1041052
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1041052-9
PII: S 0002-9947(1993)1041052-9
Article copyright: © Copyright 1993 American Mathematical Society