The aim of this book is to give a survey of results in the theory of algebraic numbers
achieved in the first half of the twentieth century and may be viewed as a companion to my …

Peter Borwein had wide-ranging mathematical interests, and was a pioneer in
computational and experimental investigations in many areas. We fondly recall some of his …

A polynomial f∈ ℂ [z] is unimodular if all its coefficients have unit modulus. Let U n denote
the set of unimodular polynomials of degree n− 1, and let U n∗ denote the subset of …

Mahler's problem asks for the largest possible value of the Mahler measure, normalized by
the $ L_2 $ norm, of a polynomial with $\pm1 $ coefficients and large degree. We establish a …

A Survey on the Conjecture of Lehmer and the Conjecture of Schinzel-Zassenhaus Page 1 HAL
Id: hal-02315014 https://hal.science/hal-02315014 Preprint submitted on 14 Oct 2019 HAL is a …

The conjecture of Lehmer is proved to be true. The proof mainly relies upon:(i) the properties
of the Parry Upper functions $ f_ {house (\alpha)}(z) $ associated with the dynamical zeta …

The height of an algebraic number A is a measure of how arithmetically complicated A is.
We say A is totally p-adic if the minimal polynomial of A splits completely over the field of p …

This text is addressed to readers who are already engaged in their own research in the
problem of Lehmer in at least one domain concerned, like graduate students, post-docs and …

Abstract [eng] The doctoral dissertation deals with mathematical problems related to various
heights of polynomials. The height of a polynomial, in the most general sense, is a quantity …