Dedekind sums arising from newform Eisenstein series Academic Article

abstract

• For primitive nontrivial Dirichlet characters [Formula: see text] and [Formula: see text], we study the weight zero newform Eisenstein series [Formula: see text] at [Formula: see text]. 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 [Formula: see text]. We also give a short proof of the reciprocity formula for this Dedekind sum.

authors

• Young, Matthew

published proceedings

• INTERNATIONAL JOURNAL OF NUMBER THEORY

altmetric score

• 0.25

author list (cited authors)

• Stucker, T., Vennos, A., & Young, M. P.

citation count

• 3

complete list of authors

• Stucker, T||Vennos, A||Young, MP

publication date

• November 2020

publisher

• World Scientific Publishing  Publisher

keywords

• Dedekind Sums
• Eisenstein Series
• Newform
• Reciprocity Formula

Digital Object Identifier (DOI)

• 10.1142/S1793042120501092

start page

• 2129

end page

• 2139

volume

• 16

issue

• 10

URL

• http://dx.doi.org/10.1142/s1793042120501092