Travis Dillon, Stephanie Gaston
Published 2019-07-26Version 1
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.
A new explicit formula in the additive theory of primes with applications II. The exceptional set in Goldbach's problem
On the moduli of a Dedekind sum
An explicit formula for Bernoulli numbers in terms of Stirling numbers of the second kind
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