On Lehmer's Problem and Hyperbolic Geometry

Explore a 54-minute lecture from the 1st Brazilian Workshop in Analytic Number Theory where Mikhail Belolipetsky from IMPA delves into the connections between Lehmer's problem and hyperbolic geometry. Part of a broader workshop bringing together number theory researchers from across Brazil, the presentation contributes to a program featuring international speakers discussing various aspects of analytic and algebraic number theory, including topics like convolution of periodic multiplicative functions, low-lying zeros in families of CM elliptic curves, and the geometry of Markov and Lagrange spectra. Delivered at IMPA in Rio de Janeiro during the October-November 2024 workshop, the lecture represents one component of an initiative to foster collaboration and showcase current number theory research in Brazil.