## Stephanie Chan, University of Michigan

January 15th, 2021 2:30-3:30 pm CET

**Title** : A density of ramified primes

**Abstract** : Let $K$ be a cyclic number field of odd degree over ℚ with odd narrow class number, such that $2$ is inert in $K$/ℚ. We extend the definition of spin (a special quadratic residue symbol) to all odd ideals in $K$, 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.