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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.