This is proved in G. Tenenaum's book (introduction to analytic and probabilistic number theory), page 39 (section 3.3, theorem 3). I agree that Gronwall's paper, other than the fact that it studies the same function, seem to be completely unrelated.

This is proved in G. Tenenbaum's book (Introduction to analytic and probabilistic number theory), page 39 (section 3.3, theorem 3). I agree that Gronwall's paper, other than the fact that it studies the same function, seem to be completely unrelated.