Eisenstein series associated with Γ0 (2)

Journal Article

In this paper, we define the normalized Eisenstein series P, e, and Q associated with Γ0(2), and derive three differential equations satisfied by them from some trigonometric identities. By using these three formulas, we define a differential equation depending on the weights of modular forms on Γ0(2) and then construct its modular solutions by using orthogonal polynomials and Gaussian hypergeometric series. We also construct a certain class of infinite series connected with the triangular numbers. Finally, we derive a combinatorial identity from a formula involving the triangular numbers. © 2008 Springer Science+Business Media, LLC.

Full Text

Duke Authors

Cited Authors

  • Hahn, H

Published Date

  • 2008

Published In

Volume / Issue

  • 15 / 2

Start / End Page

  • 235 - 257

International Standard Serial Number (ISSN)

  • 1382-4090

Digital Object Identifier (DOI)

  • 10.1007/s11139-007-9075-z