Explicit calculations with Eisenstein series Academic Article

abstract

• 2018 Elsevier Inc. We find explicit change-of-basis formulas between Eisenstein series attached to cusps, and newform Eisenstein series attached to pairs of primitive Dirichlet characters. As a consequence, we prove a BruggemanKuznetsov formula for newforms of square-free level and trivial nebentypus. We also derive, in explicit form, the Fourier expansion, Hecke eigenvalues, AtkinLehner pseudo-eigenvalues, and other data associated to these Eisenstein series, with arbitrary integer weight, level, and nebentypus.

authors

• Young, Matthew

published proceedings

• JOURNAL OF NUMBER THEORY

altmetric score

• 0.5

author list (cited authors)

• Young, M. P.

citation count

• 16

complete list of authors

• Young, Matthew P

publication date

• January 2019

publisher

• Elsevier  Publisher

published in

• Journal of Number Theory  Journal

keywords

• Bruggeman-kuznetsov Formula
• Cusps
• Eisenstein Series
• Fourier Coefficients
• Newforms

Digital Object Identifier (DOI)

• 10.1016/j.jnt.2018.11.007

start page

• 1

end page

• 48

volume

• 199

URL

• http://dx.doi.org/10.1016/j.jnt.2018.11.007