Results 261 to 270 of about 73,475 (298)
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Primes, Arithmetic Functions, and the Zeta Function
2002In this chapter we will discuss properties of primes and prime decomposition in the ring A = F[T]. Much of this discussion will be facilitated by the use of the zeta function associated to A. This zeta function is an analogue of the classical zeta function which was first introduced by L.
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Zeta Function and the Harmonic Ontology of Prime Numbers
This article explores the ontological significance of prime numbers through the lens of the Riemann Zeta Function. By analyzing the harmonic properties and resonant patterns embedded in the distribution of prime numbers, the paper presents a novel interpretation of primes as foundational informational thresholds of reality.Rezapour, Majid, Rezapour, Ramin
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On the Lefschetz Zeta Function for a Class of Toral Maps
, 2021P. Berrizbeitia +2 more
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Goldilocks Completion: Prime-Explicit Riemann Zeta Function
We construct an analytic continuation of the Euler prime product that preserves explicit prime structure throughout the complex plane. Starting from the Euler product for real part greater than one, we develop a symmetric pairing construction using hyperbolic coordinates that extends to an entire function in Weierstrass product form.openaire +1 more source
The Distribution of Primes and the Riemann Zeta Function
1984We recall that the problem of the distribution of primes had been raised at least as far back as the Greek antiquity. The proof of our Theorem 3.9, that there are infinitely many primes, appears in Euclid (Book 9, Section 20), and Eratosthenes† devised a systematic method for obtaining all primes up to any given number x.
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Prime Bubbling Model: A Reinterpretation of Prime Generation via Riemann Zeta Function
This paper proposes a new theoretical framework, the *Prime Bubbling Model*, which reinterprets the generation of prime numbers as a dynamic energetic bubbling phenomenon emerging from the complex structure of the Riemann Zeta function. Based on AiSU Theory, primes are no longer viewed as static numerical points, but as structurally emergent entities ...openaire +1 more source
Recursive Ecology of Primes: Batesonian Models of the Zeta-Function and Prime Density
This paper explores two foundational results in analytic number theory—the RiemannHypothesis and the Prime Number Theorem—through the lens of recursive ecologicallogic derived from the Bateson Game. We model the Riemann zeta-functionas a frame-sensitive analytic ecology, in which primes serve as coherence attractorsstabilizing recursive structure ...openaire +1 more source
Quantum Prime--Zeta L-Function Universality: Solving for Dirichlet L-functions Zeros
This paper demonstrates the universal applicability of the Quantum Prime--Zeta framework by extending it to Dirichlet L-functions. Building upon the established theoretical foundation where the Riemann zeta zeros are realized as eigenvalues of a quantum prime operator, we show that the same mathematical structure---including the phenomenon of quantum ...openaire +1 more source
Connected Prime Digit Factorial Occurrences to The Riemann Zeta Function
This paper explores the theoretical relationship between the frequency of prime digits in factorial representations and the non-trivial zeros of the Riemann Zeta function. By defining the prime digit frequency within factorials and aggregating these frequencies, we propose a hypothesis where such aggregated prime digit frequencies exhibit periodic ...openaire +1 more source