Stephanie Chan, July 16, 202

Title: A density of ramified primes

Abstract: Let K be a cyclic totally real number field of odd degree over Q with odd class number, such that every totally positive unit is the square of a unit, and such that 2 is inert in K/Q. We extend the definition of spin to all odd ideals (not necessarily principal). We discuss some of the ideas involved in obtaining an explicit formula, depending only on [K:Q], for the density of rational prime ideals satisfying a certain property of spins, conditional on a standard conjecture on short character sums. This talk is based on joint work with Christine McMeekin and Djordjo Milovic.