Math @ Duke

Publications [#243561] of Heekyoung Hahn
Papers Published
 Hahn, H, Eisenstein series associated with Γ0(2),
Ramanujan Journal, vol. 15 no. 2
(February, 2008),
pp. 235257 [doi]
(last updated on 2021/06/16)
Abstract: In this paper, we define the normalized Eisenstein series P, e, and Q associated with Γ (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 Γ (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. 0 0


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