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math.NT2013★ 1 cited
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…
math.NT2013
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…
math.NT2013
A theory of theta functions to the quintic base
Tim Huber
Properties of four quintic theta functions are developed in parallel with those of the classical Jacobi null theta functions. The quintic theta functions are shown to satisfy analo…