Dedekind sums arising from newform Eisenstein series

Abstract

For primitive non-trivial Dirichlet characters ${\chi }_1$ and ${\chi }_2$, we study the weight zero newform Eisenstein series $E_{{\chi }_1,{\chi }_2}(z,s)$ at $s=1$. The holomorphic part of this function has a transformation rule that we express in finite terms as a generalized Dedekind sum. This gives rise to the explicit construction (in finite terms) of elements of $H^1({\Gamma }_0(N),\mathbb{C})$. We also give a short proof of the reciprocity formula for this Dedekind sum.

9 pages

References in corpus (2)

• Explicit calculations with Eisenstein series
• On reciprocity formula of character Dedekind sums and the integral of products of Bernoulli polynomials

Cited by in corpus (3)

• The kernel of newform Dedekind sums
• An average of generalized Dedekind sums
• Reciprocity and the Kernel of Dedekind Sums