School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Series for 1/π of level 20

Document Type

Article

Publication Date

7-2018

Abstract

Properties of theta functions and Eisenstein series dating to Jacobi and Ramanujan are used to deduce differential equations associated with McKay Thompson series of level 20. These equations induce expansions for modular forms of level 20 in terms of modular functions. The theory of singular values is applied to derive expansions for 1/π" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; font-size: 19.52px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">1/π1/� of level 20 analogous to those formulated by Ramanujan.

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Under an Elsevier user license

Publication Title

Journal of Number Theory

DOI

10.1016/j.jnt.2017.12.010

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