Department of Mathematics2024-11-1020130022-314X10.1016/j.jnt.2012.12.0012-s2.0-84874724852http://dx.doi.org/10.1016/j.jnt.2012.12.001https://hdl.handle.net/20.500.14288/17501We obtain quantitative upper bounds on partial sums of the Mobius function over semigroups of integers in an arithmetic progression. Exploiting, the cancellation of such sums, we deduce upper bounds for the discrepancy of fractions in the unit interval [0, 1] whose denominators satisfy the same restrictions. In particular, the uniform distribution and approximation of discrete weighted averages over such fractions are established as a consequence.MathematicsJournal Article1096-1658317323500006Q311033