Class number one criterion for some non-normal totally real cubic fields

2012/12/06 by Jun Ho Lee, Lee, Jun Ho
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1212.1252

9 pages

arxiv created 2012/12/06 · arxiv updated 2012/12/07

Abstract

Let \K_m\_{m≥ 4} be the family of non-normal totally real cubic number fields defined by the irreducible cubic polynomial f_m(x)=x³-mx²-(m+1)x-1, where m is an integer with m≥ 4. In this paper, we will give a class number one criterion for K_m.

Related

• Classifying multiplets of totally real cubic fields
• Simple cubic function fields and class number computations
• Cubic polynomials represented by norm forms
• A note on certain real quadratic fields with class number upto three
• Tabulation of cubic function fields via polynomial binary cubic forms