Tim Huber

Let $A(q)=\sum_{n=0}^{\infty}a_n q^n$ and $B(q)=\sum_{n=0}^{\infty}b_n q^n$ be two eta quotients. Previously, we considered the problem of when \[ a_n=0 <=> b_n=0. \] Here we consider the ``mod $m$'' version of this problem, i.e. eta…

The control of materials properties with light is a promising approach towards the realization of faster and smaller electronic devices. With phases that can be controlled via strain, pressure, chemical composition or dimensionality,…

Two level 17 modular functions $$ r=q^{2}\prod_{n=1}^{\infty}(1-q^{n})^{\left(\frac{n}{17}\right)},\quad s=q^{2}\prod_{n=1}^{\infty}\frac{(1-q^{17n})^{3}}{(1-q^{n})^{3}}, $$ are used to construct a new class of Ramanujan-Sato series for…

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…

For prime levels $5 \le p \le 19$, sets of $\Gamma_{0}(p)$-permuted theta quotients are constructed that generate the graded rings of modular forms of positive integer weight for $\Gamma_{1}(p)$. An explicit formulation of the permutation…

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 equations with interesting symmetric form. This differential system…

A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo…

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 analogues of Jacobi's quartic theta function identity and…