Giacomo Cherubini: Potential energy of totally positive algebraic integers

Abstract: We prove a new inequality involving the potential energy and the discriminant of positive real numbers. Our proof follows an argument of Siegel and is based on the method of Lagrange multipliers. When applied to the roots of an irreducible polynomial, our result gives a non-trivial estimate for the energy. This work is motivated by the Schur-Siegel-Smyth trace problem, of which we will give an overview during the talk.

For Zoom access please contact Andras Biro (biro.andras[a]renyi.hu).