Mixing
Fundamental domains of modular groups $Gamma_0(N)$
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For the modular group $Gamma_0(N)$, where $Nin mathbb{Z}_+$, there exists a fundamental domain $D_N$ which lies in the strip $-frac{1}{2} < z < frac{1}{2}$ of the upper half plane, since the translation $z rightarrow z+1$ lies in $Gamma_0(N)$. Of course, usually there are many choices of $D_N$, and I am wondering whether there exists a special choice of it that:
For every $N in mathbb{Z}_+$, there exists a $tau_N in mathbb{R}^+$ such that ${ z >tau_N, -frac{1}{2} < z < frac{1}{2}} subset D_N$, which further satisfies the property that $0$ is a limit point of the sequence ${ tau_N}$?
number-theory modular-forms
asked Jan 13 at 17:12
WenzheWenzhe
1,065410
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add a comment |
$begingroup$
For the modular group $Gamma_0(N)$, where $Nin mathbb{Z}_+$, there exists a fundamental domain $D_N$ which lies in the strip $-frac{1}{2} < z < frac{1}{2}$ of the upper half plane, since the translation $z rightarrow z+1$ lies in $Gamma_0(N)$. Of course, usually there are many choices of $D_N$, and I am wondering whether there exists a special choice of it that:
For every $N in mathbb{Z}_+$, there exists a $tau_N in mathbb{R}^+$ such that ${ z >tau_N, -frac{1}{2} < z < frac{1}{2}} subset D_N$, which further satisfies the property that $0$ is a limit point of the sequence ${ tau_N}$?
number-theory modular-forms
asked Jan 13 at 17:12
WenzheWenzhe
1,065410
$endgroup$
$begingroup$
I don't understand your question but take a look at wstein.org/Tables/fundomain/index2.html
$endgroup$
– reuns
Jan 30 at 0:22
add a comment |
$begingroup$
For the modular group $Gamma_0(N)$, where $Nin mathbb{Z}_+$, there exists a fundamental domain $D_N$ which lies in the strip $-frac{1}{2} < z < frac{1}{2}$ of the upper half plane, since the translation $z rightarrow z+1$ lies in $Gamma_0(N)$. Of course, usually there are many choices of $D_N$, and I am wondering whether there exists a special choice of it that:
For every $N in mathbb{Z}_+$, there exists a $tau_N in mathbb{R}^+$ such that ${ z >tau_N, -frac{1}{2} < z < frac{1}{2}} subset D_N$, which further satisfies the property that $0$ is a limit point of the sequence ${ tau_N}$?
number-theory modular-forms
asked Jan 13 at 17:12
WenzheWenzhe
1,065410
$endgroup$
For the modular group $Gamma_0(N)$, where $Nin mathbb{Z}_+$, there exists a fundamental domain $D_N$ which lies in the strip $-frac{1}{2} < z < frac{1}{2}$ of the upper half plane, since the translation $z rightarrow z+1$ lies in $Gamma_0(N)$. Of course, usually there are many choices of $D_N$, and I am wondering whether there exists a special choice of it that:
For every $N in mathbb{Z}_+$, there exists a $tau_N in mathbb{R}^+$ such that ${ z >tau_N, -frac{1}{2} < z < frac{1}{2}} subset D_N$, which further satisfies the property that $0$ is a limit point of the sequence ${ tau_N}$?
number-theory modular-forms
number-theory modular-forms
asked Jan 13 at 17:12
WenzheWenzhe
1,065410
asked Jan 13 at 17:12
WenzheWenzhe
1,065410
asked Jan 13 at 17:12
WenzheWenzhe
1,065410
asked Jan 13 at 17:12
WenzheWenzhe
1,065410
asked Jan 13 at 17:12
WenzheWenzhe
1,065410
1,065410
$begingroup$
I don't understand your question but take a look at wstein.org/Tables/fundomain/index2.html
$endgroup$
– reuns
Jan 30 at 0:22
add a comment |
$begingroup$
I don't understand your question but take a look at wstein.org/Tables/fundomain/index2.html
$endgroup$
– reuns
Jan 30 at 0:22
$begingroup$
I don't understand your question but take a look at wstein.org/Tables/fundomain/index2.html
$endgroup$
– reuns
Jan 30 at 0:22
$begingroup$
I don't understand your question but take a look at wstein.org/Tables/fundomain/index2.html
$endgroup$
– reuns
Jan 30 at 0:22
add a comment |
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$begingroup$
I don't understand your question but take a look at wstein.org/Tables/fundomain/index2.html
$endgroup$
– reuns
Jan 30 at 0:22