5 problems

Let a Hecke character be an algebraic Hecke character of a number field, and consider the Hecke characters attached to CM abelian varieties. CM-realization conjecture. All Hecke ch…

Let ${\mathcal {X}}$ be a $\widehat{\Gamma}$-orbit of algebraic Hecke characters over $K$, and let ${\mathcal {L}}(\lambda)$ denote the normalized algebraic Hecke $L$-value defined…

Let $F$ be a quadratic imaginary field, let $\phi$ be a Hecke character of odd weight $w$, and let $H_{\phi}$ be the pure Hodge structure associated with the motive attached to…

Let $M$ be a motive over a number field $K$ with coefficient ring $R$. It is rank one when ${\rm rank}_R(H_\sigma(M))=1$ for every embedding $\sigma:K\hookrightarrow\mathds{C}$, eq…

Let $f$ denote the congruence form whose coefficients are compared with the Atkin–Swinnerton-Dyer data for the forms $h_1,h_2$ on $\Gamma_{8^3.2^3.3^3}$. An associated congruence-f…