List questions from modular-function

Published on 10 Sep 2021 - 19:34

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Determine whether $\frac{K\left(\sqrt{1-x^2}\right)^2}{K(x)^2}$ is positive rational (given $x$)

Published on 10 Sep 2021 - 21:06

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Prove that $(3/2)^n\bmod 1\equiv (2^n-1)/2^n $ has infinitely many solutions as $n \to\infty$

Published on 10 Sep 2021 - 22:16

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Plotting graphs of Modular Forms

Published on 10 Nov 2021 - 11:45

97

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Modular function for certain upper triangular matrices (Anton Deitmar Automorphic Forms Exercise 3.4)

Published on 06 Jan 2022 - 22:09

62

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$F=\{z\in\Bbb{H}:\ |z|>1,\ 2|\Re(z)|<\lambda\}$ is fundamental domain for $G_\lambda$(the subgroup of $SL(2,\Bbb{R})$ generated by $S$ and $T_\lambda$

Published on 02 Apr 2022 - 18:52

307

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Why is j($i$) defined as $1728$ instead of $1?$

Published on 23 Oct 2022 - 15:14

116

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Doubt in application of monodromy theorem to Picard little theorem

Published on 23 Oct 2022 - 17:46

40

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Jacobi's substitution for modular equations

Published on 14 Nov 2022 - 6:51

62

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Connection between modular equation and elliptic integral

Published on 14 Nov 2022 - 7:32

119

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Asymptotics of $j$-invariant at elliptic fixed points of $\text{PSL}(2,\mathbb Z)$

Published on 25 Mar 2026 - 6:04

95

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Definition Of A Shadow

Published on 01 Jan 2023 - 13:23

List Question

$\lambda (\tau)$ as a rational function of $j(\tau)$

Determine whether $\frac{K\left(\sqrt{1-x^2}\right)^2}{K(x)^2}$ is positive rational (given $x$)

Prove that $(3/2)^n\bmod 1\equiv (2^n-1)/2^n $ has infinitely many solutions as $n \to\infty$

Plotting graphs of Modular Forms

Modular function for certain upper triangular matrices (Anton Deitmar Automorphic Forms Exercise 3.4)

$F=\{z\in\Bbb{H}:\ |z|>1,\ 2|\Re(z)|<\lambda\}$ is fundamental domain for $G_\lambda$(the subgroup of $SL(2,\Bbb{R})$ generated by $S$ and $T_\lambda$

Why is j($i$) defined as $1728$ instead of $1?$

Doubt in application of monodromy theorem to Picard little theorem

Jacobi's substitution for modular equations

Connection between modular equation and elliptic integral

Asymptotics of $j$-invariant at elliptic fixed points of $\text{PSL}(2,\mathbb Z)$

Definition Of A Shadow

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