Experimental determination of Apéry-like identities for .
Let χ be a primitive Dirichlet character of conductor q and denote by L(z,χ) the associated L-series. We provide an explicit upper bound for |L(1,χ)| when 3 divides q.
We prove that for any real there are infinitely many values of with and such thatThe proof relies on an effective version of Kronecker’s approximation theorem.