An integral approach to the Gardner-Fisher and untwisted Dowker sums
Carlos M. da Fonseca,
M. Lawrence Glasser,
Victor Kowalenko
Abstract:We present a new and elegant integral approach to computing the Gardner-Fisher trigonometric power sum, which is given bywhere m and v are positive integers. This method not only confirms the results obtained earlier by an empirical method, but it is also much more expedient from a computational point of view. By comparing the formulas from both methods, we derive several new interesting number theoretic results involving symmetric polynomials over the set of quadratic powers up to (v − 1) 2 and the generalize… Show more
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