J. Korean Math. Soc. 1999; 36(4): 707-723
Printed July 1, 1999
Copyright © The Korean Mathematical Society.
Chang Heon Kim and Ja Kyung Koo
Since the modular curve $X(4)=\Gamma(4)\backslash\frak H^*$ has genus $0$, we have a field isomorphism $K(X(4))\approx\Bbb C(j_4)$ where $j_4(z)=\theta_3(\frac z2)/\theta_4(\frac z2)$ is a quotient of Jacobi theta series (\cite{Kim-Koo3}). We derive recursion formulas for the Fourier coefficients of $j_4$ and $N(j_4)$ (=the normalized generator), respectively. And we apply these modular functions to Thompson series and the construction of class fields.
Keywords: modular functions, theta series, half integral modular forms, Thompson series, class fields
MSC numbers: 11F11, 11F22, 11R04, 11R37, 14H55
2005; 42(2): 203-222
1998; 35(4): 903-931
2016; 53(6): 1445-1457
2014; 51(2): 225-238
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd