Explicit formula for the fundamental class of functions (z, Z̃, Φ) introduced by J. Jorgenson and S. Lang, is given a new form valid for a more general fudge factor Φ. This is done for a larger class ...

Concretely, we prove explicit formulas of partial sums of the Möbius function in arithmetic progressions and partial sums of the Möbius functions on an Abelian number field. In addition, to obtain ...