Les travaux de A. Fröhlich, Ph. Cassou-Noguès et M. J. Taylor sur les bases normales
We use Bourgain's recent bound for short exponential sums to prove certain independence results related to the distribution of squarefree numbers in arithmetic progressions.
We give a simple proof that critical values of any Artin -function attached to a representation with character are stable under twisting by a totally even character , up to the -th power of the Gauss sum related to and an element in the field generated by the values of and over . This extends a result of Coates and Lichtenbaum as well as the previous work of Ward.