HI (Y ;

Let then PROPOSITION 2. 1. 2: (a) D(f, s) = i • r(s) • (211) (b) D(f, s) e 00 Ji ~ f(z)y -s s -1 L(f, s) (i 2 , O(f, s) '" -21Tny/N y s ~ a 10 e L n 0 y n =1 CD t· i' ~ (A)S . 2. A Calculus of Special Values: Let f be an arbitrary weight 2 modular form of some level.

6. 1: (a) For two cusps X,y E lP\~) <;;;:K~ let be the relative homology class represented by the projection to oriented geodesic path joining x to of the y. (b) For a primitive Dirichlet character X f. 1 to X of conductor m prime N, let Remark 1. 6. 2: There is a natural inclusion of the absolute homology of X in the relative homology: The special value A(X) actually represents an absolute homology class. To see this, consider the long exact relative homology sequence We need only show But since ~(A(X» (m, N) = 1, (see §t.

Download PDF sample

Arithmetic on Modular Curves by G. Stevens
Rated 4.22 of 5 – based on 32 votes