Linear independence result for p-adic L-values

Zusammenfassung

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 x and a number field K, the formula dim(K) (K + Sigma(s+1)(i=2), L-p (i , chi omega(1-i)) K) >= (1-epsilon) log(s)/2[K:Q](1+log 2). As a by-product, we establish an asymptotic linear independence 2[K:Q](1 +log 2) result for the values of the p-adic Hurwitz zeta function.