In "M. Kaneko and D. Zagier, A generalized Jacobi theta function and quasimodular forms, Prog. Math. 129, 165-172 (1995)" there is a proposition stating essentially that $E_2$, $E_ …

Conjecture: Let be $f$ a modular form of weight $k$ and $j$ a strictly positive integer, then the set $f,f',...,f^{(j)}$ is $\mathbb C$-linearly independent in $A$. Is that conjec …

It is well known that the graded algebra $\mathcal{M}(1)$ of Modular forms for $\Gamma = PSL_2(\mathbb{Z})$ is the polynomial algebra $$ \mathcal{M}(1) = \mathbb{C}[E_4, E_6] $$ wh …

Let $E_2$, $E_4$, and $E_6$ denote the standard Eisenstein series. The usual variables $q=e^{2\pi i\tau}$ allow us to regard the $E_n$'s as functions on either the upper half plane …

MacMahon in the paper Divisors of Numbers and their Continuations in the Theory of Partitions defines several generalized notions of the sum-of-divisors function; for example, if w …

The Eisenstein series $$ G_{2k} = \sum_{(m,n) \neq (0,0)} \frac{1}{(m + n\tau)^{2k}} $$ are modular forms (if $k>1$) of weight $2k$ and quasi-modular if $k=1$. It is clear that giv …

This problem is motivated by this question and by teaching modular polynomials for the classical modular invariant $j(\tau)$. The latter implies that if we consider the fields of …