monomocoso
New member
- Joined
- Jan 25, 2012
- Messages
- 31
Consider
\(\displaystyle x^3 + y^3 = 1
\) and let \(\displaystyle \rho \) denote the Weierstrass function.
In order to parameterize this equation, show that
\(\displaystyle x = \frac {a+b\rho'(z)}{\rho(z)}\) and \(\displaystyle y = \frac {a-b\rho'(z)}{\rho(z)}
\)
satisfy the equations for certain values of \(\displaystyle a\) and \(\displaystyle b\) and find \(\displaystyle a\) and \(\displaystyle b\) interms of \(\displaystyle g_2\) and \(\displaystyle g_3
\)
where \(\displaystyle g_2 = 60 G_4 (\omega_1, \omega_2) \)and \(\displaystyle g_3 = 140 G_6 (\omega_1, \omega_2)
\)
and \(\displaystyle G_{2k+i}\) is the Eisentstein series
\(\displaystyle x^3 + y^3 = 1
\) and let \(\displaystyle \rho \) denote the Weierstrass function.
In order to parameterize this equation, show that
\(\displaystyle x = \frac {a+b\rho'(z)}{\rho(z)}\) and \(\displaystyle y = \frac {a-b\rho'(z)}{\rho(z)}
\)
satisfy the equations for certain values of \(\displaystyle a\) and \(\displaystyle b\) and find \(\displaystyle a\) and \(\displaystyle b\) interms of \(\displaystyle g_2\) and \(\displaystyle g_3
\)
where \(\displaystyle g_2 = 60 G_4 (\omega_1, \omega_2) \)and \(\displaystyle g_3 = 140 G_6 (\omega_1, \omega_2)
\)
and \(\displaystyle G_{2k+i}\) is the Eisentstein series