M(x)=o(x) Estimates for Beurling numbers
M(x)=o(x) Estimates for Beurling numbers
In classical prime number theory there are several asymptotic formulas said to be “equivalent” to the PNT. One is the bound M(x)=o(x) for the sum function of the Moebius function. For Beurling generalized numbers, this estimate is not an unconditional consequence of the PNT. Here we give two conditions that …