Results 11 to 20 of about 67,838 (152)
A minimal integral of the Riemann $\Xi$-function [PDF]
, 2011 In this paper we obtain an equilibrium sequence $\{\omega_n\}$ for which the following holds true: the areas (measures) of the figures corresponding to the positive and negative parts, respectively, of the graph of the function $\Xi(t),\ t\in[\omega_n,\omega_{n+1}]$ are equal. Dedicated to the 500th anniversary of rabbi L\"ow.
Jan Moser
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The Generalized Riemann Hypothesis on elliptic complex fields
AIMS Mathematics, 2023 In this paper, we will introduce a new algebraic system called the elliptic complex, and consider the distribution of zeros of the function $ L(s, \chi) $ in the corresponding complex plane. The key to this article is to discover the limiting case of the
Xian Hemingway
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A monotonicity property of Riemann’s xi function and a reformulation of the Riemann hypothesis [PDF]
Periodica Mathematica Hungarica, 2010 4 pages, published ...
Sondow, Jonathan, Dumitrescu, Cristian
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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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On the Physics of the Riemann Zeros [PDF]
, 2010 We discuss a formal derivation of an integral expression for the Li coefficients associated with the Riemann xi-function which, in particular, indicates that their positivity criterion is obeyed, whereby entailing the criticality of the non-trivial zeros.
He, Yang-Hui +2 more
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Power series expansions of Riemann’s $\xi$ function [PDF]
Mathematics of Computation, 1992 High-precision values of the coefficients of power series expansions about the point \(s=1\) are obtained for the Riemann \(\xi\) function, its logarithmic derivative \(\xi'(s)/\xi(s)\), and the related functions \(\xi'(1/s)/\xi(1/s)\) and \(\log(2\xi(1/s))\).
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Gaps between zeros of the derivative of the Riemann \xi-function [PDF]
, 2009 Assuming the Riemann hypothesis, we investigate the distribution of gaps between the zeros of \xi'(s). We prove that a positive proportion of gaps are less than 0.796 times the average spacing and, in the other direction, a positive proportion of gaps ...
Bui, H. M.
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Solutions of Sign-Changing Fractional Differential Equation with the Fractional Derivatives
Abstract and Applied Analysis, 2012 We study the singular fractional-order boundary-value problem with a sign-changing nonlinear term -𝒟αx(t)=p(t)f(t,x(t),𝒟μ1x(t),𝒟μ2x(t),…,𝒟μn-1x(t ...
Tunhua Wu, Xinguang Zhang, Yinan Lu
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Riemann Xi function and equivalent of Riemann Hypothesis
, 2021 Equivalent of ...
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