Linear independence result for p-adic L-values

Abstract

The aim of this article is to provide an analogue of the Ball–Rivoal theorem for $p$-adic $L$-values of Dirichlet characters. More precisely, we prove, for a Dirichlet character $\chi$ and a number field $K$, the formula ${dim}_K(K+{\sum }_{i=2}^{s+1}{L}_p(i,\chi {\omega }^{1-i}\left)K\right)\ge \frac{(1-ϵ)log\left(s\right)}{2[K:\mathbb{Q}](1+log2)}$. As a by-product, we establish an asymptotic linear independence result for the values of the $p$-adic Hurwitz zeta function.