Resumen de A variance for k-free numbers in arithmetic progressions

R. C. Vaughan

• The second moment for the the distribution of $k$-free numbers into arithmetic progression is studied and the asymptotic formula of Hooley-Montgomery type is obtained for a wider range of values for the modulus than hitherto. In the special case of squarefree numbers this improves on the theorem of Warlimont from 1980.