On a relation to the Riemann Hypothesis and an analytic part for the divisor function

Abstract

Let phi(n) denote the Euler totient function. We study the analytic part associated with the summatory function of sigma_1(n) and obtain explicit bounds under the Riemann Hypothesis. In particular, we establish an upper bound of order x^{delta'} exp((log x)/(log log x)), where delta' = max(1/2, delta).

arXiv comment11 pages Submitted to Acta Arithmetica