Results 1 to 10 of about 3,702 (270)

Hurwitz Zeta Function Is Prime [PDF]

Mathematics, 2023
We proved that the Hurwitz zeta function is prime. In addition, we derived the Nevanlinna characteristic for this function.
Marius Dundulis, Ramūnas Garunkštis, Erikas Karikovas, Raivydas Šimėnas   +3 more
doaj   +4 more sources

An Approximation of the Prime Counting Function and a New Representation of the Riemann Zeta Function [PDF]

Mathematics
Determining 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
doaj   +3 more sources

The Ihara zeta function as a partition function for network structure characterisation [PDF]

Scientific Reports
Statistical characterizations of complex network structures can be obtained from both the Ihara Zeta function (in terms of prime cycle frequencies) and the partition function from statistical mechanics.
Jianjia Wang, Edwin R. Hancock
doaj   +2 more sources

Comparing the number of ideals in quadratic number fields

Mathematical Modelling and Control, 2022
Denote by $ a_{K}(n) $ the number of integral ideals in $ K $ with norm $ n $, where $ K $ is a algebraic number field of degree $ m $ over the rational field $ \mathcal{Q} $. Let $ p $ be a prime number.
Qian Wang, Xue Han
doaj   +1 more source

Some Observations on the Greatest Prime Factor of an Integer

Annales Mathematicae Silesianae, 2023
We examine the multiplicity of the greatest prime factor in k-full numbers and k-free numbers. We generalize a well-known result on greatest prime factors and obtain formulas related with the Riemann zeta function.
Jakimczuk Rafael
doaj   +1 more source

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
doaj   +1 more source

The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation

Journal of Nigerian Society of Physical Sciences, 2022
The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann ...
Opeyemi O. Enoch, Adejimi A. Adeniji, Lukman O. Salaudeen   +2 more
doaj   +1 more source

On the divergence of two subseries $\ldots$] {on the divergence of two subseries of $\sum\frac{1}{p}$, and theorems of de La Vall\'{e}e Poussin and Landau-Walfis

Boletim da Sociedade Paranaense de Matemática, 2022
Let $K=Q(\sqrt{d})$ be a quadratic field with discriminant $d$. It is shown that $\sum\limits_{(\frac{d}{p})=+1,_{p~ prime}}\frac{1}{p}$ and $\sum\limits_{(\frac{d}{q})=-1,_{q~ prime}}\frac{1}{q}$ are both divergent.
G. Sudhaamsh Mohan Reddy, S. Srinivas Rau, B. Uma   +2 more
doaj   +1 more source

Weyl asymptotics for perturbations of Morse potential and connections to the Riemann zeta function

Concrete Operators, 2023
Let N(T;V)N\left(T;\hspace{0.33em}V) denote the number of eigenvalues of the Schrödinger operator −y″+Vy-{y}^{^{\prime\prime} }+Vy with absolute value less than TT. This article studies the Weyl asymptotics of perturbations of the Schrödinger operator −y″
Rahm Rob
doaj   +1 more source

Some Numerical Significance of the Riemann Zeta Function

Recent Advances in Natural Sciences, 2023
In this paper, the Riemann analytic continuation formula (RACF) is derived from Euler’s quadratic equation. A nonlinear function and a polynomial function that were required in the derivation were also obtained.
Opeyemi O. Enoch, Lukman O. Salaudeen
doaj   +1 more source