Results 11 to 20 of about 19,927 (139)
Freezing transition and moments of moments of the riemann zeta function [PDF]
Quarterly Journal of Mathematics, 2023 Moments of moments of the Riemann zeta function, defined by $$ \text{MoM}_T(k,\beta) := \frac{1}{T}\int_T^{2T} \Bigg(\,\int\limits_{ |h|\leq (\log T)^\theta}|\zeta(\frac{1}{2} + i t + ih)|^{2\beta}\ dh\Bigg)^k\ dt, $$ where $k,\beta \geq 0$ and $\theta
M. Curran
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An approximation to zeros of the Riemann zeta function using fractional calculus [PDF]
Mathematics and Statistics, 2020 A novel iterative method to approximate the zeros of the Riemann zeta function is presented. This iterative method, valid for one and several variables, uses the properties of fractional calculus, in particular the fact that the fractional derivatives of
A. Torres-Hernandez, F. Brambila-Paz
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Volumes of spheres and special values of zeta functions of $\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$ [PDF]
Acta Arithmetica, 2022 The volume of the unit sphere in every dimension is given a new interpretation as a product of special values of the zeta function of $\mathbb{Z}$, akin to volume formulas of Minkowski and Siegel in the theory of arithmetic groups.
A. Karlsson, Massimiliano Pallich
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An elementary proof of Ramanujan's identity for odd zeta values [PDF]
Journal of Classical Analysis, 2021 The Riemann zeta function ζ(s) is one of the most important special functions of Mathematics. While the critical strip 0 < R (s) < 1 is undoubtedly the most important region in the complex plane on account of the unsolved problem regarding location of ...
Sarth Chavan
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Fractional parts and their relations to the values of the Riemann zeta function [PDF]
Arabian Journal of Mathematics, 2017 A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant.
Ibrahim M. Alabdulmohsin
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On the correlation of shifted values of the Riemann zeta function [PDF]
, 2009 In 2007, assuming the Riemann Hypothesis (RH), Soundararajan \cite{Moment} proved that $\int_{0}^T |\zeta(1/2 + it)|^{2k} dt \ll_{k, \epsilon} T(\log T)^{k^2 + \epsilon}$ for every $k$ positive real number and every $\epsilon > 0.$ In this paper we ...
Vorrapan Chandee
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On the Sign of the Real Part of the Riemann Zeta Function [PDF]
Number Theory and Related Fields, 2012 We consider the distribution of the argument of the Riemann zeta function on vertical lines with real part greater than 1/2, and in particular two densities related to the argument and to the real part of the zeta function on such lines.
J. A. D. Reyna, R. Brent, J. Lune
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Applicable Analysis and Discrete Mathematics, 2023 We first study some generalizations of Eulerian fractions with complex order parameter and investigate their interrelationship with likewise generalized Eulerian functions as well as Stirling functions.
P. Butzer, T. He, C. Markett
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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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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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