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
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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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A renormalization approach to the Riemann zeta function at — 1, 1 + 2 + 3 + …~ — 1/12.
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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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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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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Hybrid moments of the Riemann zeta-function [PDF]
, 2014 The "hybrid" moments $$ \int_T^{2T}|\zeta(1/2+it)|^k{(\int_{t-G}^{t+G}|\zeta(1/2+ix)|^\ell dx)}^m dt $$ of the Riemann zeta-function $\zeta(s)$ on the critical line $\Re s = 1/2$ are studied.
Iftikhar A. Burhanuddin +1 more
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Moments of the Riemann zeta function on short intervals of the critical line [PDF]
, 2019 We show that as $T\to \infty$, for all $t\in [T,2T]$ outside of a set of measure $\mathrm{o}(T)$, $$ \int_{-(\log T)^{\theta}}^{(\log T)^{\theta}} |\zeta(\tfrac 12 + \mathrm{i} t + \mathrm{i} h)|^{\beta} \mathrm{d} h = (\log T)^{f_{\theta}(\beta ...
Arguin, Louis-Pierre +2 more
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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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Riemann zeta function and quantum chaos
, 2007 A brief review of recent developments in the theory of the Riemann zeta function inspired by ideas and methods of quantum chaos is given.Comment: Lecture given at International Conference on Quantum Mechanics and Chaos, Osaka, September ...
Bogomolny, Eugene
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