Results 31 to 40 of about 106,424 (299)
Comparing the number of ideals in quadratic number fields
Mathematical Modelling and Control, 2022 Denote by $ a_{K}(n) $ the number of integral ideals in $ K $ with norm $ n $, where $ K $ is a algebraic number field of degree $ m $ over the rational field $ \mathcal{Q} $. Let $ p $ be a prime number.
Qian Wang, Xue Han
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Journal of Mathematics Research, 2023 We prove the Countably Infinite Subsets of odd primes have cardinality of Arbitrarily Large in Number. This is achieved by demonstrating the asymptotic law of distribution of prime numbers that involves natural logarithm function to be applicable to all ...
John Y. C. Ting
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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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Some Observations on the Greatest Prime Factor of an Integer
Annales Mathematicae Silesianae, 2023 We examine the multiplicity of the greatest prime factor in k-full numbers and k-free numbers. We generalize a well-known result on greatest prime factors and obtain formulas related with the Riemann zeta function.
Jakimczuk Rafael
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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 +2 more
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Orbit Growth of Shift Spaces Induced by Bouquet Graphs and Dyck Shifts
Mathematics, 2021 For a discrete dynamical system, the prime orbit and Mertens’ orbit counting functions describe the growth of its closed orbits in a certain way. The asymptotic behaviours of these counting functions can be determined via Artin–Mazur zeta function of the
Azmeer Nordin, Mohd Salmi Md Noorani
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The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation
Journal of Nigerian Society of Physical Sciences, 2022 The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann ...
Opeyemi O. Enoch +2 more
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Gaps between primes, and the pair correlation of zeros of the zeta-function [PDF]
Acta Arithmetica, 1982 D. R. Heath‐Brown
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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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On the logarithm of the Riemann zeta-function near the nontrivial zeros [PDF]
Transactions of the American Mathematical Society, 2020 Assuming the Riemann hypothesis and Montgomery's Pair Correlation Conjecture, we investigate the distribution of the sequences $(\log|\zeta(\rho+z)|)$ and $(\arg\zeta(\rho+z)).$ Here $\rho=\frac12+i\gamma$ runs over the nontrivial zeros of the zeta ...
Fatma Cicek
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