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Strong -analogues for values of the Dirichlet beta function
Ankush Goswami, Timothy Huber
An infinite class of relations between modular forms is constructed that generalizes evaluations of the Dirichlet beta function at odd positive integers. The work is motivated by a…
Level Ramanujan-Sato series
Tim Huber, Dan Schultz, Dongxi Ye
Two level 17 modular functions are us…
Series for of signature 20
Tim Huber, Dan Schultz, Dongxi Ye
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. Thes…
Balanced modular parameterizations
Tim Huber, Danny Lara, Esteban Melendez
For prime levels , sets of -permuted theta quotients are constructed that generate the graded rings of modular forms of positive integer weight for $Γ_{1}…
Differential equations for septic theta functions
Tim Huber, Danny Lara
We demonstrate that quotients of septic theta functions appearing in S. Ramanujan's Notebooks and in F. Klein's work satisfy a new coupled system of nonlinear differential equation…
On cubic multisections of Eisenstein series
Andrew Alaniz, Tim Huber
A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restric…