Results 21 to 30 of about 5,990,152 (267)

On positive sequences of reals whose block sequence has an asymptotic distribution function [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper we study the properties of the unbounded sequence 0≤y₁≤y₂≤y₃≤... of positive reals having asymptotic distribution function of the form x^λ.
József Bukor, Ferdinánd Filip, János T. Tóth   +2 more
doaj   +1 more source

On the Zeros of the Differential Polynomial φ(z)f2(z)f′(z)2 − 1

Mathematics, 2019
In this study, the value distribution of the differential polynomial φ f 2 f ′ 2 − 1 is considered, where f is a transcendental meromorphic function, φ ( ≢ 0 ) is a small function of f by the reduced counting ...
Junfeng Xu, Shuichao Ye
doaj   +1 more source

Multiplicative Inequalities for Primes and the Prime Counting Function

, 2022
See the abstract in the attached pdf.
openaire   +2 more sources

Arithmetic functions, prime counting function and polynomials [PDF]

Mathematical Inequalities & Applications, 2012
In this paper we prove some properties regarding classical arithmetic functions and the prime counting function in connection with polynomials. More specific, this paper deals with composition between arithmetic functions or between the prime counting function and a polynomial and we study when some of these kind of compositions are rational functions ...
Cezar Lupu, Vlad Matei
openaire   +1 more source

Asymptotic expansions of the prime counting function [PDF]

Journal of Number Theory, 2022
We provide several asymptotic expansions of the prime counting function $π(x)$ and related functions. We define an {\it asymptotic continued fraction expansion} of a complex-valued function of a real or complex variable to be a possibly divergent continued fraction whose approximants provide an asymptotic expansion of the given function.
openaire   +2 more sources

Generalised prime systems with periodic integer counting function [PDF]

, 2012
We study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare.
Titus Hilberdink, Hilberdink, Titus
core   +1 more source

SOME EXPRESSIONS OF THE SMARANDACHE PRIME FUNCTION [PDF]

, 2000
The main purpose of this paper is using elementary arithmetical functions to give some expressions of the Smarandache Prime Function P(n)
Ruiz, Sebastian Martin
core   +1 more source

Applications of Smarandache Function, and Prime and Coprime Functions [PDF]

, 2002
A book for people who love numbers: Smarandache Function applied to perfect numbers, congruences.
Ruiz, Sebastián Martín
core   +1 more source

On certain inequalities for the prime counting function [PDF]

Notes on Number Theory and Discrete Mathematics, 2021
We study certain inequalities for the prime counting function π(x). Particularly, a new proof and a refinement of an inequality from [1] is provided.
openaire   +1 more source

A Scale Invariant Distribution of the Prime Numbers

Computation, 2015
The irregular distribution of prime numbers amongst the integers has found multiple uses, from engineering applications of cryptography to quantum theory.
Wayne S. Kendal, Bent Jørgensen
doaj   +1 more source