Journal of Algebra, Number Theory: Advances and ApplicationsAuthor's: Y.-F. S. Pétermann
Pages: [1] - [9]
Received Date: February 22, 2011
Submitted by: Dae San Kim
An unsubstantiated 1958 claim of Vinogradov [15] and Korobov [8]
concerning the remainder term in the prime number theorem, never
clearly withdrawn by its authors, has been widely reproduced in the
literature since then and still occasionally appears even in serious
publications.
Korobov’s paper [8] is also linked with another less familiar
controversy regarding two asymptotic estimates of a sum involving the
Euler 
due respectively to Walfisz [19] and
Saltykov [13].
My two purposes here are to offer some comments on the first issue,
based on bibliographic references, and to settle the second one by
pointing out a mistake in [13]. This note is largely based on a talk I
gave a few years ago at seminars and at a conference.
Euler’s function’s average, Weyl’s exponential sums, prime number theorem, zeros of the zeta function.
