Saad El Boukhari

A Coates-Sinnott-type Theorem for First Derivatives of Artin $L$-Functions

Let $K/k$ be a finite abelian extension of number fields with Galois group $G$ and let $n\geq 2$. We prove, assuming the relevant $p$-part of the equivariant Tamagawa number conjecture, first-derivative analogues of the Deligne-Ribet integrality theorem and of the Coates-Sinnott conjecture. We construct a rank-one lead...