Results 1 to 10 of about 5,990,152 (267)
The Fractal Nature of an Approximate Prime Counting Function [PDF]
Fractal and Fractional, 2017 Prime number related fractal polygons and curves are derived by combining two different aspects. One is an approximation of the prime counting function build on an additive function.
Dimitris Vartziotis, Joachim Wipper
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On certain inequalities for the prime counting function – Part III [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 As a continuation of [10] and [11], we offer some new inequalities for the prime counting function π(x). Particularly, a multiplicative analogue of the Hardy–Littlewood conjecture is provided. Improvements of the converse of Landau's inequality are given.
József Sándor
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Primes and the Lambert W function
Mathematics, 2018 The Lambert W function, implicitly defined by W ( x ) e
Matt Visser
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MathematicsDetermining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev’s estimates, etc.) particularly valuable.
Timothy Ganesan
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New properties of divisors of natural number [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The divisors of a natural number are very important for several areas of mathematics, representing a promising field in number theory. This work sought to analyze new relations involving the divisors of natural numbers, extending them to prime numbers ...
Hamilton Brito da Silva
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Orbit Growth of Shift Spaces Induced by Bouquet Graphs and Dyck Shifts
Mathematics, 2021 For a discrete dynamical system, the prime orbit and Mertens’ orbit counting functions describe the growth of its closed orbits in a certain way. The asymptotic behaviours of these counting functions can be determined via Artin–Mazur zeta function of the
Azmeer Nordin, Mohd Salmi Md Noorani
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Identities Arising from Binomial-Like Formulas Involving Divisors of Numbers
Annales Mathematicae Silesianae, 2023 In this article, we derive a great number of identities involving the ω function counting distinct prime divisors of a given number n. These identities also include Pochhammer symbols, Fibonacci and Lucas numbers and many more.
Gryszka Karol
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Combinatorial Models of the Distribution of Prime Numbers
Mathematics, 2021 This work is divided into two parts. In the first one, the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial ...
Vito Barbarani
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Ramanujan-type congruences modulo 4 for partitions into distinct parts
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 In this paper, we consider the partition function Q(n) counting the partitions of n into distinct parts and investigate congruence identities of the form Q(p⋅n+p2-124)≡0 (mod4),Q\left( {p \cdot n + {{{p^2} - 1} \over {24}}} \right) \equiv 0\,\,\,\left(
Merca Mircea
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Prime numbers with a certain extremal type property
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2019 The convex hull of the subgraph of the prime counting function x → π(x) is a convex set, bounded from above by a graph of some piecewise affine function x → ε(x). The vertices of this function form an infinite sequence of points (ek,π(ek))1∞.
Edward Tutaj
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