Results 21 to 30 of about 3,702 (270)

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
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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
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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
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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
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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
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Distribution of primes represented by polynomials and Multiple Dedekind zeta functions

, 2022
n this paper, we state several conjectures regarding distribution of primes and of pairs of primes represented by irreducible homogeneous polynomial in two variables $f(a,b)$. We formulate conjectures with respect to the slope $t=b/a$ for any irreducible polynomial $f$. Here, we formulate a conjecture for all irreducible polynomials.
Ivan Horozov, Nickola Horozov, Zouberou Sayibou   +2 more
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The recurrence formulas for primes and non-trivial zeros of the Riemann zeta function

, 2020
In this article, we explore the Riemann zeta function with a perspective on primes and non-trivial zeros. We develop the Golomb's recurrence formula for the $n$th+1 prime, and assuming (RH), we propose an analytical recurrence formula for the $n$th+1 non-trivial zero of the Riemann zeta function.
Artur Kawalec
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Twin Primes and the Zeros of the Riemann Zeta Function

, 2012
The Legendre type relation for the counting function of ordinary twin primes is reworked in terms of the inverse of the Riemann zeta function. Its analysis sheds light on the distribution of the zeros of the Riemann zeta function in the critical strip and their links to primes and the twin prime problem.
Hans J. Weber
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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
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Prime Reciprocal Digit Frequencies and the Euler Zeta Function

, 2009
6 ...
Subhash Kak
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