FUNCTION : getaprodcuspORDS - ORD of generalized-etaproduct at each cusp
CALLING SEQUENCE : getaprodcuspORDS()
getaprodcuspORDS(L,cusps,wids)
PARAMETERS : L - (geta)-list produced by GETAP2getalist
cusps - Set of inequivalent cusps for Gamma[1](N).
wids - List of corresponding widths.
GLOBAL VARIABLES : toterror - total ORD (should be zero)
xprint (default=false)
SYNOPSIS : Let G be a generalized-etaproduct corresponding to the
getalist L. This proc calculates ORD(G,z) with respect to
Gamma[1](N) for each cusp z in cusps. Here cusps is a list
of inequivalent cusps of Gamma[1](N) and wids is the list
of their corresponding widths. The cusp at infinity is
repesented by oo. The total ORD should be 0.
Global var toterror = total ORD (for error-checking).
If xprint is true then extra info is printed.
EXAMPLES :
> with(thetaids):
>
> getaprodcuspORDS();
-------------------------------------------------------------
getaprodcuspORDS(L,cusps,wids)
Let G be a generalized-etaproduct corresponding to the
getalist L. This proc calculates ORD(G,z) with respect to
Gamma[1](N) for each cusp z in cusps. Here cusps is a list
of inequivalent cusps of Gamma[1](N) and wids is the list
of their corresponding widths. The cusp at infinity is
repesented by oo. The total ORD should be 0.
Global var toterror = total ORD (for error-checking).
-------------------------------------------------------------
> CW40:=CUSPSANDWIDMAKE1(40):
> jptmp:=1/JAC(3,40,infinity)*JAC(5,40,infinity)^2*JAC(6,40,infinity)^2
> /JAC(7,40,infinity)/JAC(8,40,infinity)^2/JAC(12,40,infinity)^3
> /JAC(13,40,infinity)*JAC(14,40,infinity)^2
> *JAC(15,40,infinity)^2*JAC(16,40,infinity)^2/JAC(17,40,infinity)
> /JAC(20,40,infinity):
> eptmp:=jac2eprod(jptmp);
2 2 2 2 2
eptmp := GETA(40, 5) GETA(40, 6) GETA(40, 14) GETA(40, 15) GETA(40, 16)
/ 2 3
/ (GETA(40, 3) GETA(40, 7) GETA(40, 8) GETA(40, 12) GETA(40, 13)
/
GETA(40, 17) GETA(40, 20))
> gltmp:=GETAP2getalist(eptmp);
gltmp := [[40, 3, -1], [40, 5, 2], [40, 6, 2], [40, 7, -1], [40, 8, -2],
[40, 12, -3], [40, 13, -1], [40, 14, 2], [40, 15, 2], [40, 16, 2],
[40, 17, -1], [40, 20, -1]]
> Gamma1ModFunc(gltmp,40);
1
> getaprodcuspORDS(gltmp,CW40[1],CW40[2]);
[0, 0, 0, 0, -2, 3, 0, 0, 1, 0, -4, 0, -2, 0, 0, 3, 1, 0, 0, 0, 0, 0, -2, 0, 1,
-2, 1, -2, 1, 3, 3, 1, 1, -2, -2, 0, 1, -2, 1, -4, 0, 0, 0, 0, 1, 1, 1, 0]
>
> xprint:=true:
> getaprodcuspORDS(gltmp,CW40[1],CW40[2]);
Cusp ords:
[[oo, 0], [0, 0], [1/2, 0], [1/3, 0], [1/4, -2], [1/5, 3], [1/6, 0], [1/7, 0],
[1/8, 1], [1/9, 0], [1/10, -4], [1/11, 0], [1/12, -2], [1/13, 0], [1/14, 0],
[1/15, 3], [1/16, 1], [1/17, 0], [1/18, 0], [1/19, 0], [1/20, 0], [2/5, 0],
[3/4, -2], [3/5, 0], [3/8, 1], [3/10, -2], [3/16, 1], [3/20, -2], [3/40, 1],
[4/5, 3], [4/15, 3], [5/8, 1], [7/8, 1], [7/10, -2], [7/12, -2], [7/15, 0],
11
[7/16, 1], [7/20, -2], [7/40, 1], [9/10, -4], [9/20, 0], [9/40, 0], [--, 0],
40
13 13 13 17 19
[--, 0], [--, 1], [--, 1], [--, 1], [--, 0]]
15 16 40 40 40
TOTAL ORD = 0
[0, 0, 0, 0, -2, 3, 0, 0, 1, 0, -4, 0, -2, 0, 0, 3, 1, 0, 0, 0, 0, 0, -2, 0, 1,
-2, 1, -2, 1, 3, 3, 1, 1, -2, -2, 0, 1, -2, 1, -4, 0, 0, 0, 0, 1, 1, 1, 0]
DISCUSSION :
SEE ALSO :