Trigonometric sums through Ramanujan’s theory of theta functions

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...

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Bibliographic Details
Published inThe Ramanujan journal Vol. 57; no. 3; pp. 931 - 948
Main Authors Harshitha, K. N., Vasuki, K. R., Yathirajsharma, M. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2022
Springer Nature B.V
Subjects
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions (mathematics)
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Sums
Trigonometric sums
Ramanujan’s general theta function
Modular equations
11F20
11L03
33C75
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Summary: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.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-020-00349-9