Results 151 to 160 of about 31,208 (175)

Sums of reciprocals of general divisor functions and the Selberg divisor problem

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1991
For the ordinary \(m\)-dimensional divisor function \(d_ m(n)\), \textit{J. M. De Koninck} and \textit{A. Ivić} [Topics in arithmetical functions. Amsterdam etc.: North-Holland (1980; Zbl 0442.10032)] proved that \[ \sum_{n\leq x}\frac{1}{d_ m(n)}= x\sum^{N}_{k=0}A_ k^*(\log x)^{1/m-k-1}+O_ N(x(\log x)^{1/m-N-2}) \tag{1} \] where \(x\) is a large real ...
openaire   +2 more sources

A property of convolution sum for divisor functions

AIP Conference Proceedings, 2012
In this article, we shall give a generalization of the formula Σk = 1N−1σ1(2nk)σ3(2n(N−k)).
Daeyeoul Kim, Aeran Kim
openaire   +1 more source

On the Average of the Sum-of-odd-divisors Function

2002
In the present paper, we study the error term in the average of the sum-of-odd-divisors function σ’(n) which is defined by \(\sigma '(n) = {\sum _{_{d\,odd}^{d|n}}}\). More precisely, we study the fluctuation in the error term in the average S 1 ’ (x) = Σn≤xσ’(n).
ADHIKARI S. D, COPPOLA, Giovanni
openaire   +2 more sources

Sums of Higher Divisor Functions with Almost Equal Variables

Frontiers of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

A NEW UPPER BOUND FOR THE SUM OF DIVISORS FUNCTION

Bulletin of the Australian Mathematical Society, 2017
Robin’s criterion states that the Riemann hypothesis is true if and only if $\unicode[STIX]{x1D70E}(n)<e^{\unicode[STIX]{x1D6FE}}n\log \log n$ for every positive integer $n\geq 5041$. In this paper we establish a new unconditional upper bound for the sum of divisors function, which improves the current best unconditional estimate given by Robin. For
openaire   +1 more source

The sum of divisors function and the Riemann hypothesis

Ramanujan Journal, 2021
Jean-Louis Nicolas
exaly  

On power values of sum of divisors function in arithmetic progressions

Indian Journal of Pure and Applied Mathematics, 2023
Vidyanshu Mishra
exaly  

Arithmetic properties of the sum of divisors

Journal of Number Theory, 2021
Tewodros Amdeberhan, Victor H Moll, Diego Villamizar   +2 more
exaly  

On the sum of divisors function

Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, 2013
openaire   +1 more source

On the sum-of-divisors function

The Fibonacci Quarterly, 2007
openaire   +1 more source