Resumen de Computations in non-commutative Iwasawa theory

Tim Dokchitser, Vladimir Dokchitser

• We study special values of $L$-functions of elliptic curves over $\mathbb{Q}$ twisted by Artin representations that factor through a false Tate curve extension $\mathbb{Q} (\mu_{p^\infty}, \sqrt[p^\infty]m) / \mathbb{Q}$. In this setting, we explain how to compute $L$-functions and the corresponding Iwasawa-theoretic invariants of non-abelian twists of elliptic curves. Our results provide both theoretical and computational evidence for the main conjecture of non-commutative Iwasawa theory.