Monday, September 27, 2021 12:30 PM
Alex Smith (Stanford)

The absolute trace of a totally positive algebraic integer is defined to be the average of its conjugate elements in \$\mathbb{R}\$. We show that there are infinitely many totally positive algebraic integers of absolute trace at most \$1.81\$ but only finitely many of absolute trace at most \$1.80\$. Previously, it was only known that there are infinitely many totally positive algebraic integers of absolute trace at most \$2\$. The infinite family of totally positive integers with small trace is constructed non-explicitly via a combination of geometry of numbers and potential theory. This talk is of work in progress.