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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 χ and a number field K, the formula dimK(K+∑i=2s+1Lp(i,χω1−i)K)≥(1−ϵ)log(s)2K:Q(1+log2). As a by-product, we establish an asymptotic linear independence result for the values of the p-adic Hurwitz zeta function.
Johannes Sprang (Tue,) studied this question.