On the CM character of the curves y(2)=x(q)-1

[摘要] For most odd primes q we present an explicit formula for the number of points on the curve y(2)=x(q)-1 modulo p. The description is similar to Gauss's formula for the case q=3. The result follows from a determination of the CM character of the curve. The only q that are excluded are those rare ones for which 2(q)=2 mod q(2). (C) 1997 Academic Press.

[发布日期] 1997-05-01