Finite Trigonometric Character Sums Via Discrete Fourier Analysis

Details Finite Trigonometric Character Sums Via Discrete Fourier Analysis Finite Trigonometric Character Sums Via Discrete Fourier Analysis

2008-04-04

arxiv.org/abs/0804.0645v2

International Journal of Number Theory 6, no. 1 (2010), 51-67

Mathematics

Number Theory

14 pages

Scientific paper

We prove several old and new theorems about finite sums involving characters and trigonometric functions. These sums can be traced back to theta function identities from Ramanujan's notebooks and were systematically first studied by Berndt and Zaharescu; their proofs involved complex contour integration. We show how to prove most of Berndt-Zaharescu's and some new identities by elementary methods of discrete Fourier Analysis.

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