An average of generalized Dedekind sums

Travis Dillon; Stephanie Gaston

doi:10.1016/j.jnt.2019.11.008

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arXiv · 1907.11745

An average of generalized Dedekind sums

Travis Dillon·Stephanie Gaston

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Abstract

We study a generalization of the classical Dedekind sum that incorporates two Dirichlet characters and develop properties that generalize those of the classical Dedekind sum. By calculating the Fourier transform of this generalized Dedekind sum, we obtain an explicit formula for its second moment. Finally, we derive upper and lower bounds for the second moment with nearly identical orders of magnitude.

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Travis Dillon, Stephanie Gaston. 2019-07-26. An average of generalized Dedekind sums. https://doi.org/10.1016/j.jnt.2019.11.008

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