Abstract
We determine the limiting distribution of the family of values L′L(1/2+ϵ,χD) as D varies over fundamental discriminants. Here, 0<ϵ<12, and χD is the real character associated with D. Moreover, we also establish an upper bound for the rate of convergence of this family to its limiting distribution. As a consequence of this result, we derive an asymptotic bound for the small values of |L′L(1/2+ϵ,χD)|.
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