Results 21 to 30 of about 106,424 (299)
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
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
doaj +1 more source
Beurling Zeta Functions, Generalised Primes, and Fractal Membranes [PDF]
Acta Applicandae Mathematicae, 2004 We study generalised prime systems $\mathcal{P ...
Titus Hilberdink, Michel L. Lapidus
openalex +5 more sources
Jost function, prime numbers and Riemann zeta function
, 2003 The large complex zeros of the Jost function (poles of the S matrix) in the complex wave number-plane for s-wave scattering by truncated potentials are associated to the distribution of large prime numbers as well as to the asymptotic behavior of the imaginary parts of the zeros of the Riemann zeta function on the critical line.
S. Joffily
openalex +4 more sources
Contributions to the theory of the riemann zeta-function and the theory of the distribution of primes [PDF]
Acta Mathematica, 1916 n ...
G. H. Hardy, J. E. Littlewood
openalex +4 more sources
The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta-Function [PDF]
International Journal of Number Theory, 2023 In this paper, we prove an unconditional form of Fujii's formula for the average number of Goldbach representations and show that the error in this formula is determined by a general zero-free region of the Riemann zeta-function, and vice versa.
Keith Billington +3 more
semanticscholar +1 more source
Mean values of the logarithmic derivative of the Riemann zeta‐function near the critical line [PDF]
Mathematika, 2022 Assuming the Riemann hypothesis and a hypothesis on small gaps between zeta zeros (see equation (ES 2K) below for a precise definition), we prove a conjecture of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith [J. Math. Phys.
F. Ge
semanticscholar +1 more source
Lower bounds for negative moments of ζ′(ρ)$\zeta ^{\prime }(\rho )$ [PDF]
Mathematika, 2022 We establish lower bounds for the discrete 2kth moment of the derivative of the Riemann zeta function at nontrivial zeros for all ...
Peng Gao, Liangyi Zhao
semanticscholar +1 more source
Gocgen Approach for Zeta Function in Twin Primes
International Journal of Pure and Applied Mathematics ResearchI 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
Twenty Digits of Some Integrals of the Prime Zeta Function
, 2008 The double sum sum_(s >= 1) sum_p 1/(p^s log p^s) = 2.00666645... over the inverse of the product of prime powers p^s and their logarithms, is computed to 24 decimal digits. The sum covers all primes p and all integer exponents s>=1. The calculational strategy is adopted from Cohen's work which basically looks at the fraction as the underivative ...
Richard J. Mathar
openalex +4 more sources