3 problems

Let $M$ be an $L$-admissible premotivic structure over $K$, let $\tau:K\to\mathbb{C}$ be an embedding, and let $\lambda$ be any finite prime of $K$. Write…

Let $M$ be an object of the category of premotivic structures over $K$ that is $L$-admissible at every prime. Let $L(M,s)$ be its $K\otimes\mathbb{C}$-valued $L$-function, let…

Fix number fields $K,L$ and a pure motive $M$ of weight $w$ over $K$ with coefficients in $L$. Let $L(s,M)$ be its motivic $L$-function, let $L_{\infty}(s,M)$ be its archimedean fa…