Results 21 to 30 of about 70,351 (225)

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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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
doaj  

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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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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Speiser’s Theorem on the Road

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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Physics of the Riemann Hypothesis

, 2011
Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics.
Ablowitz, M. J., Aczel, A. D., Alfaro, V. D., Arnol’d, V. I., Berry, M. V., Berry, M. V., Bhaduri, R. K., Bohigas, O., Bohigas, O., Borwein, P., Brack, M., Böhm, A., Celletti, A., Chadan, K., Cipra, B., Cvitanović, P., David A. W. Hutchinson, de la Vallée-Poussin, C. J., Dickson, L. E., Drake, S., Dyson, F., Dániel Schumayer, Eckhardt, B., Einstein, A., Elizalde, E., Elizalde, E., Euler, L., Flügge, S., Gelfand, I. M., Gutzwiller, M. C., Hadamard, J., Hadamard, J., Hardy, G. H., Hardy, G. H., Hejhal, D. A., Hejhal, D. A., Huang, K., Ivic, A., Joffily, S., Julia, B., Kanemitsu, S., Kotnik, T., Lapidus, M. L., Mehta, M. L., Montgomery, H. L., Newton, R. G., Press, W. H., Ribenboim, P., Ribenboim, P., Riemann, B., Riemann, B., Schnirelman, A. I., Stöckmann, H.-J., Titchmarsh, E. C., Vardi, I., Xianxi, D.   +55 more
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Numerical Calculations to Grasp a Mathematical Issue Such as the Riemann Hypothesis

Information, 2020
This article presents the use of data processing to apprehend mathematical questions such as the Riemann Hypothesis (RH) by numerical calculation. Calculations are performed alongside graphs of the argument of the complex numbers ζ ( x + i y ...
Michel Riguidel
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New Analytical Formulas for the Rank of Farey Fractions and Estimates of the Local Discrepancy

Mathematics
New analytical formulas are derived for the rank and the local discrepancy of Farey fractions. The new rank formula is applicable to all Farey fractions and involves sums of a lower order compared to the searched one.
Rogelio Tomás García
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