Results 21 to 30 of about 640,811 (318)

Along the Lines of Nonadditive Entropies: q-Prime Numbers and q-Zeta Functions [PDF]

Entropy, 2021
The rich history of prime numbers includes great names such as Euclid, who first analytically studied the prime numbers and proved that there is an infinite number of them, Euler, who introduced the function ζ(s)≡∑n=1∞n−s=∏pprime11−p−s, Gauss, who ...
Ernesto P. Borges, Takeshi Kodama, C. Tsallis   +2 more
semanticscholar   +6 more sources

Prime pairs and the zeta function

Journal of Approximation Theory, 2008
AbstractAre there infinitely many prime pairs with given even difference? Most mathematicians think so. Using a strong arithmetic hypothesis, Goldston, Pintz and Yildirim have recently shown that there are infinitely many pairs of primes differing by at most sixteen.There is extensive numerical support for the prime-pair conjecture (PPC) of Hardy and ...
Jacob Korevaar
openalex   +4 more sources

Arithmetic forms of Selberg zeta functions with applications to prime geodesic theorem [PDF]

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2002
We obtain an arithmetic expression of the Selberg zeta function for cocompact Fuchsian group defined via an indefinite division quaternion algebra over $\mathbf{Q}$. As application to the prime geodesic theorem, we prove certain uniformity of the distribution.
Tsuneo Arakawa, Shin-ya Koyama, Maki Nakasuji   +2 more
openalex   +4 more sources

Contributions to the theory of the riemann zeta-function and the theory of the distribution of primes [PDF]

Acta Mathematica, 1916
n ...
G. H. Hardy, J. E. Littlewood
openalex   +5 more sources

Gocgen Approach for Zeta Function in Twin Primes

International Journal of Pure and Applied Mathematics Research
I had previously developed an approach called Gocgen approach, which claimed to prove twin prime conjecture. In this paper, I processed the previously developed Gocgen approach with the zeta function and explained the relationship between the zeta function with some formulas to offer another perspective on the zeta function, and also created a new ...
Ahmet F. Gocgen
  +4 more sources

Jost function, prime numbers and Riemann zeta function

, 2003
The large complex zeros of the Jost function (poles of the S matrix) in the complex wave number-plane for s-wave scattering by truncated potentials are associated to the distribution of large prime numbers as well as to the asymptotic behavior of the imaginary parts of the zeros of the Riemann zeta function on the critical line.
S. Joffily
openalex   +4 more sources

Zero-free strips for the Riemann zeta-function derived from the Prime Number Theorem [PDF]

arXiv, 2020
We use the Prime Number Theorem to prove the existence of zero-free strips for the Riemann-zeta function. Precisely, we prove that there exists $\delta>0$ for which if $0\leq r<\delta $ then $\zeta(s)\neq 0$ for Re$(s)>1-r$.
Douglas Azevedo
arxiv   +3 more sources

Zeta-functions of harmonic theta-series and prime numbers [PDF]

St. Petersburg Mathematical Journal, 2012
Speaking on rational prime numbers in various arithmetical sequences, it may be noted that no essential progress have been achieved for more than century and a half since famous Dirichlet theorem on prime numbers in arithmetic progressions (1837). Absolutely mystical is still the question on prime numbers in quadratic sequences, i.e., on prime numbers ...
A. S. Andrianov
openalex   +3 more sources

On a prime zeta function of a graph [PDF]

Pacific Journal of Mathematics, 2015
Takehiro Hasegawa, S. Saito
semanticscholar   +3 more sources

The Mean Square of the Hurwitz Zeta-Function in Short Intervals

Axioms
The Hurwitz zeta-function ζ(s,α), s=σ+it, with parameter ...
Antanas Laurinčikas, Darius Šiaučiūnas   +1 more
doaj   +2 more sources