On mod p nonvanishing of special values of L-functions associated with cusp forms on GL2 over imaginary quadratic fields

Abstract

Let $f$ be a cusp form on ${GL}_2$ over an imaginary quadratic field $F$ of class number 1, and let $p$ be an odd prime which satisfies some mild conditions. Then we show the existence of a finite-order Hecke character $\phi$ of $F_{\mathbf{A}}^{\times }$ such that the algebraic part of the special value of $L$-functions of $f\otimes \phi$ at $s=1$ is a $p$-adic unit. This is an analogous result to the result of A. Ash and G. Stevens for ${GL}_2$ over the field of rationals obtained in [AS].