The Fourier transform of trigonometric functions on the multiplicative group <inline-formula><tex-math id="M1">\begin{document}${\mathbb Z}^{\times}(m)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2019-math-023_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2019-math-023_M1.png"/></alternatives></inline-formula>

SHEN Lichien

doi:10.3969/j.issn.1000-5641.201911023

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Nov. 2020

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

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

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

doi: 10.3969/j.issn.1000-5641.201911023

SHEN Lichien

1.
Department of Mathematics, University of Florida, Gainesville FL　32611-8105, USA

Received Date: 2019-05-21
Publish Date: 2020-11-25

Abstract

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.
- character,
- Fourier transform,
- Gauss sum,
- Kronecker symbol,
- theta function

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References(5)

References

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