Modular forms and Eisenstein's continued fractions

JOURNAL OF NUMBER THEORY

卷:117

Article

Folsom, A

关键词: modular forms;    continued fractions;    q-series;    basic hypergeometric series;   

DOI  :  10.1016/j.jnt.2005.06.001

来源: Elsevier

【 摘 要 】

Found in the collected works of Eisenstein are twenty continued fraction expansions. The expansions have since emerged in the literature in various forms, although a complete historical account and self-contained treatment has not been given. We provide one here, motivated by the fact that these expansions give continued fraction expansions for modular forms. Eisenstein himself did not record proofs for his expansions, and we employ only standard methods in the proofs provided here. Our methods illustrate the exact recurrence relations from which the expansions arise, and also methods likely similar to those originally used by Eisenstein to derive them. (c) 2005 Elsevier Inc. All fights reserved.

【 授权许可】

Free