Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function [PDF]
Combinatorics, Probability and Computing, 2022 AbstractWe study approximations for the Lévy area of Brownian motion which are based on the Fourier series expansion and a polynomial expansion of the associated Brownian bridge. Comparing the asymptotic convergence rates of the Lévy area approximations, we see that the approximation resulting from the polynomial expansion of the Brownian bridge is ...
James Foster, Karen Habermann
semanticscholar +7 more sources
A renormalization approach to the Riemann zeta function at — 1, 1 + 2 + 3 + …~ — 1/12. [PDF]
AIMS Mathematics, 2018 A scaling and renormalization approach to the Riemann zetafunction, $\zeta$, evaluated at $-1$ is presented in two ways. In the first,one takes the difference between $U_{n}:=\sum_{q=1}^{n}q$ and$4U_{\left\lfloor \frac{n}{2}\right\rfloor }$ where $\left ...
Gunduz Caginalp
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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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The Quantum Mellin transform [PDF]
, 2006 We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum ...
Bateman H +15 more
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Riemann Zeroes and Phase Transitions via the Spectral Operator on Fractal Strings [PDF]
, 2012 The spectral operator was introduced by M. L. Lapidus and M. van Frankenhuijsen [La-vF3] in their reinterpretation of the earlier work of M. L. Lapidus and H. Maier [LaMa2] on inverse spectral problems and the Riemann hypothesis.
Herichi, Hafedh, Lapidus, Michel L.
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Linear law for the logarithms of the Riemann periods at simple critical zeta zeros [PDF]
, 2006 Each simple zero 1/2 + iγn of the Riemann zeta function on the critical line with γn > 0 is a center for the flow s˙ = ξ(s) of the Riemann xi function with an associated period Tn. It is shown that, as γn →∞, log Tn ≥ π/4 γn + O(log γn).
Barnett, A. Ross, Broughan, Kevin A.
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Fast methods to compute the Riemann zeta function [PDF]
, 2011 The Riemann zeta function on the critical line can be computed using a straightforward application of the Riemann-Siegel formula, Sch\"onhage's method, or Heath-Brown's method.
Hiary, Ghaith Ayesh
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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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Statistical properties of zeta functions' zeros [PDF]
, 2014 The paper reviews existing results about the statistical distribution of zeros for the three main types of zeta functions: number-theoretical, geometrical, and dynamical.
Kargin, Vladislav
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Truncated Infinitesimal Shifts, Spectral Operators and Quantized Universality of the Riemann Zeta Function [PDF]
, 2013 We survey some of the universality properties of the Riemann zeta function $\zeta(s)$ and then explain how to obtain a natural quantization of Voronin's universality theorem (and of its various extensions).
Herichi, Hafedh, Lapidus, Michel L.
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