Monogenic cubic rings and Thue equations

Abstract: Let K be a cubic number field. We give an absolute upper bound for the number of monogenic orders which have small index (compared to the discriminant of K) in the ring of integers of K. This is done by counting the number of integral solutions of some cubic Thue equations. This reduction to the resolution of Thue equations will also allow us to count the number of monogenic orders with a fixed index in the ring of integers of K.

algebraic geometrynumber theory

Audience: researchers in the topic

Comments: Meeting ID: 908 611 6889, Passcode: The order of the symmetric group on 9 elements (Type the 6-digit number)

FGC-HRI-IPM Number Theory Webinars

Series comments: password is 848084