5 problems

Higher-order switching conjecture.

Let $K$ be a number field containing the $\ell$-th roots of unity, let $\mathcal{O}_K$ be its ring of integers, and let $\mathcal{F}_\ell$ be a family of Hecke characters of order…

Let $K$ be a number field containing the $\ell$-th roots of unity, let $\mathcal{O}_K$ be its ring of integers, and let $\mathcal{F}_\ell$ be a family of Hecke characters of order…

Let $K=\mathbf{Q}(\sqrt{-n})$ and let $X>1$. In the prime ideal theorem for Gr"o{ss}encharaktere over $K$, an exceptional primitive quadratic Gr"o{ss}encharakter…

Let $H_{\mathfrak{c}}$ be the ray class group modulo $\mathfrak{c}$, let $R_{\mathfrak{c}}:= H_{\mathfrak{c}} \otimes \mathbb{Z}/n\mathbb{Z}$, and let $\psi$ and $\psi'$ be charact…