Results 11 to 20 of about 31,208 (175)

Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52

Open Mathematics, 2017
The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
doaj   +2 more sources

On the number of prime factors of values of the sum-of-proper-divisors function [PDF]

Journal of Number Theory, 2015
Let $\omega(n)$ (resp. $\Omega(n)$) denote the number of prime divisors (resp. with multiplicity) of a natural number $n$. In 1917, Hardy and Ramanujan proved that the normal order of $\omega(n)$ is $\log\log n$, and the same is true of $\Omega(n ...
Troupe, Lee
core   +2 more sources

Euler's function and the sum of divisors.

Journal für die reine und angewandte Mathematik (Crelles Journal), 1981
openaire   +3 more sources

Dynamic multi‐objective optimisation of complex networks based on evolutionary computation

IET Networks, EarlyView., 2022
Abstract As the problems concerning the number of information to be optimised is increasing, the optimisation level is getting higher, the target information is more diversified, and the algorithms are becoming more complex; the traditional algorithms such as particle swarm and differential evolution are far from being able to deal with this situation ...
Linfeng Huang
wiley   +1 more source

N $$ \mathcal{N} $$ = 2* Schur indices

Journal of High Energy Physics, 2023
We find closed-form expressions for the Schur indices of 4d N $$ \mathcal{N} $$ = 2* super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with
Yasuyuki Hatsuda, Tadashi Okazaki
doaj   +1 more source

Arithmetic convolution sums derived from eta quotients related to divisors of 6

Open Mathematics, 2022
The aim of this paper is to find arithmetic convolution sums of some restricted divisor functions. When divisors of a certain natural number satisfy a suitable condition for modulo 12, those restricted divisor functions are expressed by the coefficients ...
Ikikardes Nazli Yildiz, Hwang Jihyun, Kim Daeyeoul   +2 more
doaj   +1 more source

Average order of the divisor functions with negative power weight [PDF]

, 1993
In this paper we are primarily concerned with the study of the sums of the sum-of-divisors function σn(n) with negative power weight n-1(t>0), i.e. the sums of the form ..
Ishibashi Makoto
core   +1 more source

Tau function and moduli of differentials [PDF]

, 2011
The tau function on the moduli space of generic holomorphic 1-differentials on complex algebraic curves is interpreted as a section of a line bundle on the projectivized Hodge bundle over the moduli space of stable curves.
Korotkin, Dmitry, Zograf, Peter
core   +1 more source

Some new arithmetic functions [PDF]

Notes on Number Theory and Discrete Mathematics
We introduce and study some new arithmetic functions, connected with the classical functions φ (Euler's totient), ψ (Dedekind's function) and σ (sum of divisors function).
József Sándor, Krassimir Atanassov
doaj   +1 more source

Extremal orders of some functions connected to regular integers modulo n

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013
Let V (n) denote the number of positive regular integers (mod n) less than or equal to n. We give extremal orders of , , , , where σ(n), ψ(n) are the sum-of-divisors function and the Dedekind function, respectively. We also give extremal orders for and ,
Brăduţ Apostol
doaj   +1 more source