Norm and trace of the j-invariants of Drinfeld modules associated to hyperelliptic curves

[摘要] Let k/F-q(x) be a quadratic extension that is ramified over the unique pole of x, and let A be the integral closure of F-q[x] in k. Then k is the function field analogue of an imaginary quadratic number field. A rank-one Drinfeld A-module phi of generic characteristic is the analogue of an elliptic curve with complex multiplications by the full ring of integers of an imaginary quadratic number field. In this paper, we compute the degrees of the trace and norm down to F-q[x] of j(phi), the j-invariant of phi. Our results generalize previous ones where k was assumed to have genus g = 1. (C) 1997 Academic Press.

[发布日期] 1997-03-01