CMI PhD Research Seminar
Date: Tuesday, 22 October 2024
Time: 02:00 - 03:00 PM
Venue: Seminar Hall
Algebraic numbers close to both 0 and 1
Suhita Hazra
Chennai Mathematical Institute.
22-10-24

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Abstract

In 1933, Lehmer conjectured that the relative height of an algebraic number    a which is not a root of unity is bounded away from 0. This is still open. In this connection Zhang has proved H(a) + H(1 − a) ≥ C for some positive constant C (except for a known finite set of values of a),    where H(a) denotes the absolute (logarithmic) height of a. In this talk, we will discuss an elementary proof of this result, given by Zagier.