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 +3 more
doaj +5 more sources
Prime zeta function statistics and Riemann zero-difference repulsion [PDF]
Journal of Statistical Mechanics: Theory and Experiment, 2021 We present a derivation of the numerical phenomenon in which differences between the Riemann zeta function’s nontrivial zeros tend to avoid being equal to the imaginary parts of the zeros themselves, a property called statistical ‘repulsion’ between the ...
Gordon Chavez, Altan Allawala
semanticscholar +6 more sources
A note on prime zeta function and Riemann zeta function. Corrigendum [PDF]
Notes on Number Theory and Discrete Mathematics, 2021 In [1] the author proposed two new results concerning the prime zeta function and the Riemann zeta function but they turn out to be wrong. In the present paper we provide their correct form.
Mladen Vassilev-Missana
semanticscholar +3 more sources
Twin Primes and the Zeros of the Riemann Zeta Function [PDF]
arXiv, 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
arxiv +5 more sources
The recurrence formulas for primes and non-trivial zeros of the Riemann zeta function [PDF]
arXiv, 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
arxiv +5 more sources
Prime Reciprocal Digit Frequencies and the Euler Zeta Function [PDF]
arXiv, 2009 Some open questions related to prime reciprocal digit frequencies with potential applications to cryptography are presented.
Subhash Kak
arxiv +5 more sources
An Approximation of the Prime Counting Function and a New Representation of the Riemann Zeta Function [PDF]
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
doaj +3 more sources
Prime number theory and the Riemann Zeta-function [PDF]
, 2005 Heath-Brown, D. R.
core +6 more sources
Distribution of Beurling primes and zeroes of the Beurling zeta function I. Distribution of the zeroes of the zeta function of Beurling [PDF]
, 2020 We consider the oscillation properties of the remainder term $\Delta(x)$ in the prime number formula for Beurling primes, and their relation to the distribution of the nontrivial zeroes of the Beurling zeta function $\zeta$.
Szilárd Gy. Révész
semanticscholar +5 more sources
Prime product formulas for the Riemann zeta function and related identities [PDF]
arXiv, 2019 In this article, we derive a Euler prime product formula for the magnitude of the Riemann zeta function $\zeta(s)$ valid for $\Re(s)>1$, as well as similar formulas for $\zeta(s)$ valid for an even and odd $k$th positive integer argument. We shall further give a set of generated formulas for $\zeta(k)$ up to $11$th order, including Ap\'ery's constant ...
Artur Kawalec
arxiv +5 more sources