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Results tagged with transcendental-number-theory
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user 123157
3
votes
0
answers
76
views
Algebraic independece of modular forms for Fricke group over $\mathbb C(q)$
Let $q=e^{\pi i \tau}$ for $\tau \in \mathbb H$ and
$$
P_2(q)=\frac{P(q)+2P(q^2)}{3}, \quad Q_2(q)=\frac{Q(q)+4Q(q^2)}{5}, \\ R_2(q)=\frac{R(q)+8R(q^2)}{9},
$$
a Fourier series of quasi-modular form …
- 663
9
votes
1
answer
626
views
Algebraic independence of $P,Q,R$ or $E_2,E_4,E_6$ over $\mathbb C(z)$
Let $P,Q,R$ be the Fourier series of the Eisenstein series $E_2,E_4,E_6$, that is,
$$
P(q)=1-24\sum_{n=1}^{\infty}\sigma_1(n)q^n,
$$
$$
Q(q)=1+240\sum_{n=1}^{\infty}\sigma_3(n)q^n,
$$
$$
R(q)=1-504 …
- 663
11
votes
Accepted
Algebraic independence of $P,Q,R$ or $E_2,E_4,E_6$ over $\mathbb C(z)$
I think the following answers the question. It does not depend on the above comments because I didn't understand them. This is just my approach.
(But not fully my idea because it depends on a strong p …
- 663