A density of ramified primes

Abstract: Let $K$ be a cyclic number field of odd degree over $\mathbb{Q}$ with odd narrow class number, such that $2$ is inert in $K/\mathbb{Q}$. 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 $[K:\mathbb{Q}]$, 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.

algebraic geometryalgebraic topologycategory theorydifferential geometrygeneral topologynumber theoryprobability

Audience: researchers in the topic

( slides | video )

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ZORP (zoom on rational points)

Series comments: 2 talks on a Friday, roughly once per month.

Online coffee break in between.

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