Abstract
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.
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The authors would like to thank the referee for comments that improved the quality of the paper and also for bringing the article [5] to their attention.
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The first author is supported by Grant UGC-Ref. No.: 982/(CSIR-UGC NET DEC.2017) by the funding agency UGC, INDIA, under CSIR-UGC JRF. The second author is supported by Grant No. F. 510/12/DRS-II/2018 (SAP-I) by the University Grants Commission, India. The third author is supported by Grant No. 09/119(0221)/2019-EMR-1 by the funding agency CSIR, INDIA, under CSIR-JRF.
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Harshitha, K.N., Vasuki, K.R. & Yathirajsharma, M.V. Trigonometric sums through Ramanujan’s theory of theta functions. Ramanujan J 57, 931–948 (2022). https://doi.org/10.1007/s11139-020-00349-9
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DOI: https://doi.org/10.1007/s11139-020-00349-9