Publications [#243561] of Heekyoung Hahn

Papers Published

1. Hahn, H, Eisenstein series associated with Gamma_0(2), Ramanujan J., vol. 15 no. 2 (2008), pp. 235-257 [doi]
   (last updated on 2024/04/22)

   Abstract:
   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.