The mean square of the divisor function

Abstract

Let d(n) be the divisor function. In 1916, S. Ramanujan stated but without proof that n≤x

On the Balog-Ruzsa Theorem in short intervals

“…The proof of Lemma 3.1 is motivated by the methods used in dealing with the Dirichlet divisor problem, see e.g. [6]. In the above proof, we combine analytic methods with hyperbolic trick and van der Corput bounds.…”

Contributions of Ramachandra to the Theory of the Riemann Zeta-Function

“…For an improvement of (7.3), the readers are referred to [JiSa14]. As such it looks to be a challenging problem to reduce the exponent 5 of the factor log x in (7.3).…”

Exponential and Infinitary Divisors

“…Equation (10) implies that τ ∞ (n) is even for n = 1. Then for p > 2, a > 1 the value of σ (e)∞ (p a ) is a sum of even number of odd summands and is even.…”