Results 31 to 40 of about 640,811 (318)
Twenty Digits of Some Integrals of the Prime Zeta Function
, 2008 The double sum sum_(s >= 1) sum_p 1/(p^s log p^s) = 2.00666645... over the inverse of the product of prime powers p^s and their logarithms, is computed to 24 decimal digits. The sum covers all primes p and all integer exponents s>=1. The calculational strategy is adopted from Cohen's work which basically looks at the fraction as the underivative ...
Richard J. Mathar
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Zeta functions and asymptotic additive bases with some unusual sets of primes [PDF]
The Ramanujan Journal, 2015 Fix $ \in(0,1]$, $ _0\in[0,1)$ and a real-valued function $\varepsilon(x)$ for which $\limsup_{x\to\infty}\varepsilon(x)\le 0$. For every set of primes ${\mathcal P}$ whose counting function $ _{\mathcal P}(x)$ satisfies an estimate of the form $$ _{\mathcal P}(x)= \, (x)+O\bigl(x^{ _0+\varepsilon(x)}\bigr),$$ we define a zeta function $ _ ...
William D. Banks
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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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Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH [PDF]
Mathematics of Computation, 2015 Followed referee's advice including changing ...
Loïc Grenié, Giuseppe Molteni
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On the prime zeta function and the Riemann hypothesis
, 2019 By considering the prime zeta function, the author intended to demonstrate in that the Riemann zeta function zeta(s) does not vanish for Re(s)>1/2, which would have proven the Riemann hypothesis. However, he later realised that the proof of "Theorem 3" is fundamentally flawed.
Tatenda Kubalalika
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The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta-Function [PDF]
International Journal of Number Theory, 2023 In this paper, we prove an unconditional form of Fujii's formula for the average number of Goldbach representations and show that the error in this formula is determined by a general zero-free region of the Riemann zeta-function, and vice versa.
Keith Billington +3 more
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Mean values of the logarithmic derivative of the Riemann zeta‐function near the critical line [PDF]
Mathematika, 2022 Assuming the Riemann hypothesis and a hypothesis on small gaps between zeta zeros (see equation (ES 2K) below for a precise definition), we prove a conjecture of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith [J. Math. Phys.
F. Ge
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Lower bounds for negative moments of ζ′(ρ)$\zeta ^{\prime }(\rho )$ [PDF]
Mathematika, 2022 We establish lower bounds for the discrete 2kth moment of the derivative of the Riemann zeta function at nontrivial zeros for all ...
Peng Gao, Liangyi Zhao
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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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