Abstract The monotonicity of entropy is investigated for real quadratic rational maps on the circle R ∪ { ∞ stretchy="...

The principal topic of this article is to extend Shanks' infrastructure ideas in real quadratic number elds to the case of real quadratic congruence function elds. In this view, this paper is intended as a \low-brow" approach to the theory of ideals and operations in the ideal class group. We summarize some basic properties of ideals and provide elementary proofs of the main results. For the pu...

For a quartic primitive CM field K, we say that a rational prime p is evil if at least one of the abelian varieties with CM by K reduces modulo a prime ideal p|p to a product of supersingular elliptic curves with the product polarization. We call such primes evil primes for K. In [GL], we showed that for fixed K, such primes are bounded by a quantity related to the discriminant of the field K. ...