Abstract
We consider Dirichlet L-functions L(s, chi ) where chi is a non-principal quadratic character to the modulus q. We make explicit a result due to Pintz and Stephens by showing that |L(1, chi )|leqslant frac{1}{2}log q for all qgeqslant 2cdot 10^{23} and |L(1, chi )|leqslant frac{9}{20}log q for all qgeqslant 5cdot 10^{50}.
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