Algebraicity of L-values for elliptic curves in a false Tate curve tower

Thanasis Bouganis, Vladimir Dokchitser

Let $E$ be an elliptic curve over $Q$, and $\tau$ an Artin representation over $Q$ that factors through the non-abelian extension $Q(\sqrt[p^n]{m},{\mu }_{p^n})/Q$, where $p$ is an odd pri…