- Open Access
Distribution of orders in number fields
© Kaplan et al.; licensee Springer. 2015
Received: 14 August 2014
Accepted: 15 April 2015
Published: 10 June 2015
In this paper, we study the distribution of orders of bounded discriminants in number fields. We use the zeta functions introduced by Grunewald, Segal, and Smith. In order to carry out our study, we use p-adic and motivic integration techniques to analyze the zeta function. We give an asymptotic formula for the number of orders contained in the ring of integers of a quintic number field. We also obtain non-trivial bounds for higher degree number fields.
AMS Subject Classification: Primary 11M41; 11R29; secondary 11S40