On partial sums of the M\"obius and Liouville functions for number   fields
  Landau examined the partial sums of the M\"obius function and the Liouville function for a number field $K$. First we shall try again the same problem by using a new Perron's formula due to Liu and Ye. Next we consider the equivalent theorem of the grand Riemann hypothesis for the Dedekind zeta-function of $K$ and that of the prime ideal theorem. 
Yusuke Fujisawa, Makoto Minamide
math.NT