FUNCTION : v0 - 2*ORD(G,0)
CALLING SEQUENCE : v0(L,N)
PARAMETERS : L - (geta)-list produced by GETAP2getalist
and corresponds to a generalized eta-quotient
on Gamma[1](N).
N - positive integer
SYNOPSIS : Returns 2*ORD(G,0) where G is the generalized eta-quotient
corresponding to the (geta)-list L with respect to the
group GAMMA[1](N).
EXAMPLES :
> with(thetaids):
> v0();
-------------------------------------------------------------
v0(L,N)
L is a getalist; i.e. L=[[b1,a1,c1],....]
Let G be the corresponding generalized eta-function.
v0(L,N) returns 2*ORD(G,0, Gamma[1](N))
-------------------------------------------------------------
> jterm:=q^3*JAC(2,40,infinity)^2/JAC(0,40,infinity)^12*JAC(3,40,infinity)
> *JAC(5,40,infinity)^2*JAC(6,40,infinity)*JAC(7,40,infinity)
> /JAC(12,40,infinity)*JAC(13,40,infinity)*JAC(14,40,infinity)
> *JAC(15,40,infinity)^2*JAC(17,40,infinity)*JAC(18,40,infinity)^2
> /JAC(20,40,infinity);
3 2 2
jterm := q JAC(2, 40, infinity) JAC(3, 40, infinity) JAC(5, 40, infinity)
JAC(6, 40, infinity) JAC(7, 40, infinity) JAC(13, 40, infinity)
2
JAC(14, 40, infinity) JAC(15, 40, infinity) JAC(17, 40, infinity)
2 / 12
JAC(18, 40, infinity) / (JAC(0, 40, infinity) JAC(12, 40, infinity)
/
JAC(20, 40, infinity))
> eprod:=jac2eprod(jterm);
2 2
eprod := GETA(40, 2) GETA(40, 3) GETA(40, 5) GETA(40, 6) GETA(40, 7)
2 2
GETA(40, 13) GETA(40, 14) GETA(40, 15) GETA(40, 17) GETA(40, 18) /(
GETA(40, 12) GETA(40, 20))
> GL:=GETAP2getalist(eprod);
GL := [[40, 2, 2], [40, 3, 1], [40, 5, 2], [40, 6, 1], [40, 7, 1], [40, 12, -1],
[40, 13, 1], [40, 14, 1], [40, 15, 2], [40, 17, 1], [40, 18, 2],
[40, 20, -1]]
> getaprodcuspord(GL,0);
1/40
> getaprodcuspord(GL,0)*cuspwid1(0,1,40);
1
> v0(GL,40);
2
> getaprodcuspord(GL,oo);
3
> getaprodcuspord(GL,oo)*cuspwid1(1,0,40);
3
> vinf(GL,40);
6
DISCUSSION : We see that v0(eprod,40) = 2 = 2*ORD(eprod,40)
SEE ALSO : jac2eprod, GETAP2getalist, rmcofjac, vinf, getaprodcuspord