Vortrag
What is… the Schinzel-Zassenhaus conjecture?
Vortrag von Alessio Cangini
Datum: 14.05.24 Zeit: 16.30 - 17.30 Raum:
''An algebraic integer is a complex number which is a root of a monic irreducible polynomial with integer coefficients. The complete set of zeros of such a polynomial is called a conjugate set of algebraic numbers. Bounding the maximum absolute value of elements in these sets from below has been studied intensively over the years by number theorists. We will call this maximum the house of an algebraic integer. In 1965, Schinzel and Zassenhaus proposed the following conjecture. There exists an absolute positive constant C such that the house of every non-zero algebraic integer which is not a root of unity is at least 1 + C/d. The above conjecture was proved in 2019 by Dimitrov. In this talk we will introduce the relevant notions and go over Dimitrov’s proof.''