乘法群<inline-formula><tex-math id="M2">\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_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2019-math-023_M2.png"/></alternatives></inline-formula>上的三角函数的傅里叶变换

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乘法群$ {\mathbb{Z}}^{\times}(m)$上的三角函数的傅里叶变换

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

摘要: 根据乘法群上的傅里叶变换理论框架, 研究了一类三角和, 并揭示了这类三角和与许多数论量 (例如高斯和、虚二次域类数和伯努利数) 之间的有趣联系.
- 特征 /
- 傅里叶变换 /
- 高斯和 /
- 克罗内克符号 /
- theta函数
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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