9 problems

Let $p$ be a prime, let $\tau\in\mathcal{H}_p$ be a real quadratic point of discriminant $D$ prime to $p$, and let $H_\tau$ be the narrow ring class field of the order defined by…

Let $\mathbb{K}$ be a number field with exactly one complex place, and consider the infinite products obtained by evaluating the geometric variants of multiple elliptic Gamma funct…

Let $K=\mathbf{Q}(\beta)$ be the complex cubic field with $\beta$ the root of $x^3-x^2+5x+1$ having positive imaginary part, let $\mathfrak{f}=(3,\beta+1)$, and let $\mathfrak{a}$…

Let $K(\mathfrak{f})$ be the relevant narrow ray class field and let $\mathbf{\Gamma}_{\mathfrak{a},h}(L)$ be the smoothed elliptic gamma value. Algebraicity conjecture. When…

Let $K$ be a complex cubic number field and let $K(\mathfrak{f})$ be the narrow ray class field of conductor $\mathfrak{f}$. Let $I(\mathfrak{f})$ be the group of fractional ideals…

Let $K$ be a complex cubic number field, let $\mathfrak{f}$ and $\mathfrak{b}$ be ideals with $(\mathfrak{f},\mathfrak{b})=1$, and set $L=\mathfrak{f}\mathfrak{b}^{-1}$. Let…

Let $K$ be an imaginary quadratic field, let $\mathfrak f$ be an ideal of $\mathcal O_K$, and let $K_{\mathfrak f}$ be the corresponding ray class field. Under the conditions of th…

Let $\Lambda$ be the Iwasawa algebra in the source, let $Q(\Lambda)$ be its total ring of fractions, and let $\Delta^\infty$ be the determinant module constructed from the inverse…

Let $K obreakbullet$ be the relevant tower of number fields, let $mathcal{E}infty:=varprojlim(mathbb{Z}potimesmathbb{Z}mathcal{O}{Kn}^{times})$ be the inverse limit of semilocal un…