乘法群Z~×(m)上的三角函数的傅里叶变换  

The Fourier transform of trigonometric functions on the multiplicative group Z~×(m)

作　　者：沈力健 SHEN Lichien(Department of Mathematics,University of Florida,Gainesville FL 32611-8105,USA)

机构地区：[1]佛罗里达大学数学系,盖恩斯维尔FL 32611-8105,美国

出　　处：《华东师范大学学报（自然科学版）》2020年第6期1-15,共15页Journal of East China Normal University(Natural Science)

基　　金：The author would like to thank Dandan Chen for the assistance in reformatting the original manuscript to the style of the journal.

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.Based on the Fourier transform on the multiplicative group Z×(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.

关 键 词：特征 傅里叶变换 高斯和 克罗内克符号 THETA函数 

分 类 号：O174[理学—数学]