Simultaneous orderings in function fields

✍ Scribed by David Adam

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 203 KB
• Volume: 112
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2004.11.015

✦ Synopsis

For every Dedekind domain R, Bhargava defined the factorials of a subset S of R by introducing the notion of p-ordering of S, for every maximal ideal p of R. We study the existence of simultaneous ordering in the case S = R = O K , where O K is the ring of integers of a function field K over a finite field F q . We show, that when O K is the ring of integers of an imaginary quadratic extension K of F q (T ), K = F q (T )/(Y 2 -D(T )), then there exists a simultaneous ordering if and only if deg D 1.