On the Missing Log Factor

Explicit average orders: news and problems

“…The statement that (2) implies (4) is somewhat surprising and comes from E. Landau's thesis in [23], while that the statement (3) implies (4) is due to A. Axer in [1]. We shall tell more on this subject later and it is in fact the subject of the survey [39]. The statement (5) concerning the functionm is a surprising addition.…”

“…to derive bounds for M from bounds for the primes. This phenomenom is detailed in the survey [39]. This problem has been studied by A. Kienast in [22] and by L. Schoenfeld in [45], and they proceeded as the author later did in [35] by using some combinatorial identities.…”