The annihilation of divisor classes in abelian extensions of the rational function field
The arithmetic of function fields
The average rank of elliptic curves I. With Appendix "The Explicit formula for elliptic curves over function fields" by Oisín McGuinness.
The Deuring-Safarevic Formula Revisited.
The Equations for Modular Function Fields of Principal congruence subgroups of prime level.
The Galois group of the tangency problem for plane curves.
The Genus of Maximal Function Fields over Finite Fields.
The geometry of the period mapping on cyclic covers of P1
The Riemann-Roch Theorem and the Independence of the Conditions of Adjointness in the case of a curve for which the tangents at the multiple points are distinct from one another.
Theorie der algebraischen Functionen einer Veränderlichen.
Theorie der algebraischen Functionen einer Veränderlichen und der Abel'schen Integrale.
Theorie der algebraischen Functionen einer Veränderlichen und der algebraischen Integrale. Erste Abhandlung.
Torsion points in families of Drinfeld modules
Let be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a,b ∈ K[λ]. Assume that neither a(λ) nor b(λ) is a torsion point for for all λ. If there exist infinitely many λ ∈ K̅ such that both a(λ) and b(λ) are torsion points for , then we show that for each λ ∈ K̅, a(λ) is torsion for if and only if b(λ) is torsion for . In the case a,b ∈ K, we prove in addition that a and b must be -linearly dependent.