Remarks on the Póólya--Vinogradov Inequality.

We establish a numerically explicit version of the Póólya--Vinogradov inequality for the sum of values of a Dirichlet character on an interval. While the technique of proof is essentially that of Landau from 1918, the result we obtain has better constants than in other numerically explicit versions that have been found more recently. [ABSTRACT FROM AUTHOR]