Journal of East China Normal University(Natural Science) >

2020 , Vol. 2020 >Issue 6: 1 - 15

DOI: https://doi.org/10.3969/j.issn.1000-5641.201911023

Mathematics

The Fourier transform of trigonometric functions on the multiplicative group ${\mathbb Z}^{\times}(m)$

  • Lichien SHEN
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  • Department of Mathematics, University of Florida, Gainesville FL 32611-8105, USA

Received date: 2019-05-21

  Online published: 2020-12-01

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Abstract

Based on the Fourier transform on the multiplicative group $ {\mathbb Z}^{\times}(m)$, we study a class of trigonometric sums and reveal interesting connections between these sums and number theoretic quantities, such as Gauss sums, the class number of imaginary quadratic fields, and the Bernoulli number.

Key words： character; Fourier transform; Gauss sum; Kronecker symbol; theta function

Cite this article

Lichien SHEN . The Fourier transform of trigonometric functions on the multiplicative group ${\mathbb Z}^{\times}(m)$[J]. Journal of East China Normal University(Natural Science), 2020 , 2020(6) : 1 -15 . DOI: 10.3969/j.issn.1000-5641.201911023

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