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571.
Conrad Amberger 《Colloid and polymer science》1916,18(3):97-101
Ohne Zusammenfassung 相似文献
572.
For a global field K and an elliptic curve Eη over K(T), Silverman's specialization theorem implies rank(Eη(K(T)))?rank(Et(K)) for all but finitely many t∈P1(K). If this inequality is strict for all but finitely many t, the elliptic curve Eη is said to have elevated rank. All known examples of elevated rank for K=Q rest on the parity conjecture for elliptic curves over Q, and the examples are all isotrivial.Some additional standard conjectures over Q imply that there does not exist a non-isotrivial elliptic curve over Q(T) with elevated rank. In positive characteristic, an analogue of one of these additional conjectures is false. Inspired by this, for the rational function field K=κ(u) over any finite field κ with characteristic ≠2, we construct an explicit 2-parameter family Ec,d of non-isotrivial elliptic curves over K(T) (depending on arbitrary c,d∈κ×) such that, under the parity conjecture, each Ec,d has elevated rank. 相似文献
573.
A countably valued lattice-ordered group is a lattice-ordered group in which every element has only countably many values. Such lattice-ordered groups are proven to be normal-valued and, though not necessarily special-valued, every element in a countably valuedl-group must have a special value. The class of countably valuedl-groups forms a torsion class, and the torsion radical determined by this class is anl-ideal that is the intersection of all maximal countably valued subgroups.Countably valuedl-groups are shown to be closed with respect toeventually constant sequence extensions, and it is shown that many properties of anl-group pass naturally to its eventually constant sequence extension.Presented by M. Henriksen. 相似文献
574.
Brian Conrad 《Journal of Number Theory》2005,110(1):22-36
A classical conjecture of Bouniakowsky says that a non-constant irreducible polynomial in Z[T] has infinitely many prime values unless there is a local obstruction. Replacing Z[T] with κ[u][T], where κ is a finite field, the obvious analogue of Bouniakowsky's conjecture is false. All known counterexamples can be explained by a new obstruction, and this obstruction can be used to fix the conjecture. The situation is more subtle in characteristic 2 than in odd characteristic. Here, we illustrate the general theory for characteristic 2 in some examples. 相似文献
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