View More View Less
  • 1 Vilnius University Department of Mathematics and Informatics Naugarduko 24 2600 Vilnius Lithuania
Restricted access

Abstract  

We investigate the values of the Remak height, which is a weighted product of the conjugates of an algebraic number. We prove that the ratio of logarithms of the Remak height and of the Mahler measure for units αof degree d is everywhere dense in the maximal interval [d/2(d-1),1] allowed for this ratio. To do this, a “large” set of totally positive Pisot units is constructed. We also give a lower bound on the Remak height for non-cyclotomic algebraic numbers in terms of their degrees. In passing, we prove some results about some algebraic numbers which are a product of two conjugates of a reciprocal algebraic number.

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Oct 2020 0 0 0
Nov 2020 0 1 0
Dec 2020 0 0 0
Jan 2021 4 0 0
Feb 2021 0 0 0
Mar 2021 1 0 0
Apr 2021 0 0 0