Results 21 to 30 of about 67,078 (181)
The sixth moment of the Riemann zeta function and ternary additive divisor sums
Discrete Analysis, 2021 The sixth moment of the Riemann zeta function and ternary additive divisor sums, Discrete Analysis 2021:6, 60 pp. The Riemann hypothesis states that every non-trivial zero of the Riemann zeta function lies on the critical line $\Re(z) = 1/2$.
Nathan Ng
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Quantum graphs whose spectra mimic the zeros of the Riemann zeta function [PDF]
, 2014 One of the most famous problems in mathematics is the Riemann hypothesis: that the non-trivial zeros of the Riemann zeta function lie on a line in the complex plane.
Hummel, Quirin +2 more
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Fourier coefficients associated with the Riemann zeta-function
Karpatsʹkì Matematičnì Publìkacìï, 2016 We study the Riemann zeta-function $\zeta(s)$ by a Fourier series method. The summation of $\log|\zeta(s)|$ with the kernel $1/|s|^{6}$ on the critical line $\mathrm{Re}\; s = \frac{1}{2}$ is the main result of our investigation.
Yu.V. Basiuk, S.I. Tarasyuk
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On the Order of Growth of Lerch Zeta Functions
Mathematics, 2023 We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t13/84+ϵ as t → ∞.
Jörn Steuding, Janyarak Tongsomporn
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Scalar modular bootstrap and zeros of the Riemann zeta function
Journal of High Energy Physics, 2022 Using the technology of harmonic analysis, we derive a crossing equation that acts only on the scalar primary operators of any two-dimensional conformal field theory with U(1) c symmetry. From this crossing equation, we derive bounds on the scalar gap of
Nathan Benjamin, Cyuan-Han Chang
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A note on the gaps between consecutive zeros of the Riemann zeta-function [PDF]
, 2009 Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and infinitely often they differ by at least 2.69 times the average spacing ...
Bui, H. M., Milinovich, M. B., Ng, N.
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Li's criterion for the Riemann hypothesis - numerical approach [PDF]
Opuscula Mathematica, 2004 There has been some interest in a criterion for the Riemann hypothesis proved recently by Xian-Jin Li [Li X.-J.: The Positivity of a Sequence of Numbers and the Riemann Hypothesis. J. Number Theory 65 (1997), 325-333].
Krzysztof Maślanka
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On the density of some special primes
Journal of Mathematical Cryptology, 2009 We show, under the Generalized Riemann Hypothesis, that a certain set of primes which is of importance for the theory of pseudorandom sequences is of positive relative density. We also use an unconditional result of H.
Friedlander John B., Shparlinski Igor E.
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On a Fractal Representation of the Density of Primes
Recoletos Multidisciplinary Research Journal, 2014 The number of primes less or equal to a real number x, π(x), has been approximated in the past by the reciprocal of the logarithm of the number x. Such an approximation works well when x is large but it can be poor when x is small.
Joy Mirasol, Efren O. Barabat
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Walailak Journal of Science and Technology, 2019 In this note we discuss the Gauss-Lucas theorem (for the zeros of the derivative of a polynomial) and Speiser’s equivalent for the Riemann hypothesis (about the location of zeros of the Riemann zeta-function).
Janyarak TONGSOMPORN, Jörn STEUDING
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