Results 1 to 10 of about 73,475 (298)
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
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On the zero-free region and the distribution of zeros of the prime zeta function [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaThe prime zeta function is one of the most under-researched varieties of the class. Very little is known about the irregular distribution of its zeros. The presented study aims - albeit partially - to fill the gap in our understanding of the subject.
Belovas Igoris +2 more
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Selberg zeta-function associated to compact Riemann surface is prime [PDF]
Revista de la Unión Matemática Argentina, 2021 A meromorphic function \(F\) is said to be prime if for every decomposition of the form \[ F(z)=f(h(z)), \] where \(f\) is meromorphic and \(h\) is entire, one must have that either \(f\) or \(h\) is linear. The paper under review studies the Selberg-zeta function \(Z\) associated with a compact Riemann surface of genus \(g\geq 2\).
Ramūnas Garunkštis
semanticscholar +4 more sources
Prime zeta function statistics and Riemann zero-difference repulsion [PDF]
Journal of Statistical Mechanics: Theory and Experiment, 2021 Fixed more typos and minor ...
Gordon Chavez, Altan Allawala
semanticscholar +7 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.
M. Vassilev-Missana
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The prime number theorem and pair correlation of zeros of the Riemann zeta-function [PDF]
Research in Number Theory, 2022 We prove that the error in the prime number theorem can be quantitatively improved beyond the Riemann Hypothesis bound by using versions of Montgomery’s conjecture for the pair correlation of zeros of the Riemann zeta-function which are uniform in long ...
D. A. Goldston, Ade Irma Suriajaya
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Analogs of the Prime Number Problem in a Shot Noise Suppression of the Soft-Reset Process [PDF]
NanomaterialsThe soft-reset process, or a sequence of charge emissions from a floating storage node through a transistor biased in a subthreshold bias condition, is modeled by a master (Kolmogorov–Bateman) equation.
Yutaka Hirose
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The Ihara zeta function as a partition function for network structure characterisation [PDF]
Scientific ReportsStatistical 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
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Zeta function zeros, powers of primes, and quantum chaos [PDF]
Physical Review E, 2003 We present a numerical study of Riemann's formula for the oscillating part of the density of the primes and their powers. The formula is comprised of an infinite series of oscillatory terms, one for each zero of the zeta function on the critical line and was derived by Riemann in his paper on primes assuming the Riemann hypothesis.
Jamal Sakhr +2 more
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On a prime zeta function of a graph [PDF]
Pacific Journal of Mathematics, 2015 Let \(X\) be a finite graph without vertices of degree \(1\). A prime in \(X\) is a cycle (closed path) that has no subcycles of length \(2\), and cannot be obtained from another cycle by walking around it several times. Cycles that differ only by the choice of the starting point are considered equivalent and define the same prime. The authors consider
Hasegawa, Takehiro, Saito, Seiken
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