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 ...

Let 𝐾 be a function field over a finite field 𝑘 of characteristic 𝑝 and let 𝐾∞/𝐾 be a geometric extension with Galois group ℤ𝑝. Let 𝐾𝑛 be the corresponding subextension with Galois group ...