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Explicit upper bounds for |L(1,χ)| when χ(3) = 0

David J. Platt, Sumaia Saad Eddin (2013)

Colloquium Mathematicae

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.

Extremal values of Dirichlet L -functions in the half-plane of absolute convergence

Jörn Steuding (2004)

Journal de Théorie des Nombres de Bordeaux

We prove that for any real θ there are infinitely many values of s = σ + i t with σ 1 + and t + such that { exp ( i θ ) log L ( s , χ ) } log log log log t log log log log t + O ( 1 ) . The proof relies on an effective version of Kronecker’s approximation theorem.

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