Some Explicit Estimates for the Möbius Function

L(1, χ) > ce qe and all attempts at providing a value to ce for sufficiently small e have been unsuccessful. On the other hand, a wide class of functions of prime numbers have been successfully explicitly estimated during the last fifty years, starting with the benchmarking paper of Rosser and Schœnfeld [11]. For instance, refining an earlier estimate of Dusart [4], Trudgian [14] proved that, for x ≥ 229