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Results tagged with modular-forms
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user 101078
Questions about modular forms and related areas
9
votes
Accepted
Eisenstein series $E_4(z)$ and $E_6(z)$ algebraically independent over $\mathbb{C}$
First of all, $E_4$ and $E_6$ are modular forms of weights 4 and 6. Therefore, if we have $P(E_4,E_6)=0$ for some nonzero polynomial $P$, then there exists some polynomal $G$ such that $G(t^4x,t^6y)=t …
- 7,193
3
votes
Bound on an expression involving J-function coefficients
Let us define $j=J+744=\frac{1728E_4^3}{E_4^3-E_6^2}$. Then, as noted by OP, the question is equivalent to positivity of coefficients of
$$
f=q\frac{d}{dq}J+E_2(J+24)=q\frac{d}{dq}j+E_2j-720E_2.
$$
Ne …
- 7,193
4
votes
0
answers
116
views
A coefficient in Dirichlet series associated with a cofinite subgroup of $\mathrm{SL}(2,\mat...
Let $\Gamma$ be a discrete subgroup of $\operatorname{SL}(2,\mathbb R)$, acting on the upper half-plane $\mathbb H$. Suppose that $\Gamma\backslash \mathbb H$ is non-compact and its compactification $ …
- 7,193