Maximal selectivity for orders in fields

作者：Arenas Carmona Luis^*

来源：Journal of Number Theory, 2012, 132(12): 2748-2755.

DOI：10.1016/j.jnt.2012.05.031

• Central simple algebras
• Embeddings of orders
• Selectivity
• Spinor class fields
• Representation fields

If n subset of D are two orders in a central simple algebra 21 with D of maximal rank, the theory of representation fields describes the set of spinor genera of orders in the genus of D representing the order n. When n is contained in a maximal subfield of 21 and the dimension of 21 is the square of a prime p, the proportion of spinor genera representing n has the form r/p. In fact, when the representation field exists, this proportion is either 1 or 1/p. In the later case the order n is said to be selective for the genus. The condition for selectivity is known when D is maximal and also when p = 2 and D is an Eichler order. In this work we describe the orders n that are selective for at least one genus of orders of maximal rank in 21.

• 出版日期2012-12