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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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
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Selberg zeta-function associated to compact Riemann surface is prime [PDF]
Revista de la Unión Matemática Argentina, 2021 . Let Z ( s ) be the Selberg zeta-function associated to a compact Riemann surface. We consider decompositions Z ( s ) = f ( h ( s )), where f and h are meromorphic functions, and show that such decompositions can only be trivial.
Ramūnas Garunkštis
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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
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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
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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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Orbit Growth of Periodic-Finite-Type Shifts via Artin–Mazur Zeta Function
Mathematics, 2020 The prime orbit and Mertens’ orbit counting functions describe the growth of closed orbits in a discrete dynamical system in a certain way. In this paper, we prove the asymptotic behavior of these functions for a periodic-finite-type shift.
Azmeer Nordin, Mohd Salmi Md Noorani
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On the zero-free region and the distribution of zeros of the prime zeta function
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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The Mean Square of the Hurwitz Zeta-Function in Short Intervals
AxiomsThe Hurwitz zeta-function ζ(s,α), s=σ+it, with parameter ...
Antanas Laurinčikas +1 more
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