The mathematics literature contains many generalized trigonometric sums which are evaluated through contour integration methods, algebraic methods or through discrete Fourier analysis methods. The purpose of this paper is to show how Ramanujan’s theory of theta functions can be efficiently employed to evaluate certain generalized trigonometric sums. In the process, we obtain six interesting generalized trigonometric sums, that seem to be new.

中文翻译：

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通过拉马努詹的theta函数理论进行三角求和

数学文献包含许多广义三角和，可通过轮廓积分法，代数法或离散傅立叶分析法进行评估。本文的目的是说明如何有效地利用Ramanujan的theta函数理论来评估某些广义三角和。在此过程中，我们获得了六个有趣的广义三角和，它们似乎是新的。