Series for 1/π of level 20

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...

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Bibliographic Details
Published inJournal of number theory Vol. 188; pp. 121 - 136
Main Authors Huber, Tim, Schultz, Dan, Ye, Dongxi
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2018
Subjects
Dedekind eta function
Eisenstein series
Modular form
11F03
11F27
Eisenstein series
Pi
Modular form
Dedekind eta function
11F11
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Summary: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 of level 20 analogous to those formulated by Ramanujan.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2017.12.010