Transformation of Some Lambert Series and Cotangent Sums

초록

By considering a contour integral of a cotangent sum, we give a simple derivation of a transformation formula of the series A(tau,s)= Sigma(infinity)(n=1) sigma(s-1)(n)e(2 pi in tau) for complex s under the action of the modular group on tau in the upper half plane. Some special cases directly give expressions of generalized Dedekind sums as cotangent sums.

키워드