Results 31 to 40 of about 11,114,666 (310)

Inequalities between some arithmetic functions, II [PDF]

Notes on Number Theory and Discrete Mathematics
As a continuation of Part I (see [1]), we offer new inequalities for classical arithmetic functions such as the Euler's totient function, the Dedekind's psi function, the sum of the positive divisors function, the number of divisors function, extended ...
Krassimir Atanassov, József Sándor, Mladen Vassilev-Missana   +2 more
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On certain inequalities for φ, ψ, σ and related functions, III [PDF]

Notes on Number Theory and Discrete Mathematics
We obtain generalizations of certain results from [2] and [4]. The unitary variants are also considered. Some new arithmetic functions and their inequalities are also considered.
József Sándor, Karol Gryszka
doaj   +1 more source

Arithmetic functions at consecutive shifted primes [PDF]

, 2014
For each of the functions $f \in \{\phi, \sigma, \omega, \tau\}$ and every natural number $k$, we show that there are infinitely many solutions to the inequalities $f(p_n-1) < f(p_{n+1}-1) < \dots < f(p_{n+k}-1)$, and similarly for $f(p_n-1) > f(p_{n+1 ...
Pollack, Paul, Thompson, Lola
core   +2 more sources

Arithmetic functions in short intervals and the symmetric group [PDF]

Algebra & Number Theory, 2016
We consider the variance of sums of arithmetic functions over random short intervals in the function field setting. Based on the analogy between factorizations of random elements of $\mathbb{F}_q[T]$ into primes and the factorizations of random ...
B. Rodgers
semanticscholar   +1 more source

Chebyshev model arithmetic for factorable functions [PDF]

, 2016
This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating ...
Chachuat, B, Houska, B, Rajyaguru, J, Villanueva, ME   +3 more
core   +3 more sources

Integral inequalities of Hermite-Hadamard type for GA-F-convex functions

AIMS Mathematics, 2021
In the paper, the authors define a notion of geometric-arithmetic-F-convex functions and, via an integral identity and other analytic techniques, establish several integral inequalities of the Hermite-Hadamard type for geometric-arithmetic-F-convex ...
Ye Shuang, Feng Qi
doaj   +1 more source

Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
The set Set(n), generated by an arbitrary natural number n, was defined in [3]. There, and in [4], some arithmetic functions and arithmetic operators of a modal type are defined over the elements of Set(n).
Krassimir Atanassov
doaj   +1 more source

Composite Rational Functions and Arithmetic Progressions [PDF]

, 2017
In this paper we deal with composite rational functions having zeros and poles forming consecutive elements of an arithmetic progression. We also correct a result published earlier related to composite rational functions having a fixed number of zeros ...
Tengely, Szabolcs
core   +2 more sources

Ramanujan expansions of arithmetic functions of several variables [PDF]

, 2017
We generalize certain recent results of Ushiroya concerning Ramanujan expansions of arithmetic functions of two variables. We also show that some properties on expansions of arithmetic functions of one and several variables using classical and unitary ...
L. Tóth
semanticscholar   +1 more source

Two arithmetic functions related to Euler's and Dedekind's functions [PDF]

Notes on Number Theory and Discrete Mathematics
Two new arithmetic functions are introduced. In some sense, they are modifications of Euler's and Dedekind's functions. Some properties of the new functions are studied.
Krassimir Atanassov
doaj   +1 more source