Lower bound on height functions [HBNI Th288] 

Abstract

In this thesis, we investigate lower bounds for heights in connection with Lehmer’s conjecture, establishing new relationships between the Weil height and analytic objects such as the zeros of the Dedekind zeta function. Our results yield a novel criterion for Lehmer’s conjecture under the Generalized Riemann Hypothesis. In addition, we prove a p-adic equidistribution theorem for algebraic numbers of small Weil height, thereby verifying Lehmer’s conjecture for a broad class of algebraic numbers.