Affordable Access

Publisher Website

Littlewood Pisot numbers

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
117
Issue
1
Identifiers
DOI: 10.1016/j.jnt.2005.05.009
Keywords
  • Pisot And Salem Numbers
  • Littlewood Polynomials
  • Reciprocal Polynomials
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract A Pisot number is a real algebraic integer, all of whose conjugates lie strictly inside the open unit disk; a Salem number is a real algebraic integer, all of whose conjugate roots are inside the closed unit disk, with at least one of them of modulus exactly 1. Pisot numbers have been studied extensively, and an algorithm to generate them is well known. Our main result characterises all Pisot numbers whose minimal polynomial is a Littlewood polynomial, one with { + 1 ,- 1 } -coefficients, and shows that they form an increasing sequence with limit 2. It is known that every Pisot number is a limit point, from both sides, of sequences of Salem numbers. We show that this remains true, from at least one side, for the restricted sets of Pisot and Salem numbers that are generated by Littlewood polynomials. Finally, we prove that every reciprocal Littlewood polynomial of odd degree n ⩾ 3 has at least three unimodular roots.

There are no comments yet on this publication. Be the first to share your thoughts.

Statistics

Seen <100 times
0 Comments

More articles like this

Sumsets of Pisot and Salem numbers

on Expositiones Mathematicae Jan 01, 2008

The order type of the set of Pisot numbers

on Topology and its Applications Jan 01, 1996
More articles like this..