Results 21 to 30 of about 48,697 (194)
The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation
Journal of Nigerian Society of Physical Sciences, 2022 The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann ...
Opeyemi O. Enoch +2 more
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Riemann’s zeta function and beyond [PDF]
Bulletin of the American Mathematical Society, 2003 In recent years L L -functions and their analytic properties have assumed a central role in number theory and automorphic ...
Gelbart, Stephen S., Miller, Stephen D.
openaire +3 more sources
Riemann hypothesis and Zeta-Function
Bibechana, 2018 No abstract available.
Mani Raj Bhattrai
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Accurate estimation of sums over zeros of the Riemann zeta-function [PDF]
Mathematics of Computation, 2020 We consider sums of the form $\sum \phi(\gamma)$, where $\phi$ is a given function, and $\gamma$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in a given interval.
R. Brent, Dave Platt, T. Trudgian
semanticscholar +1 more source
Amplitude-like functions from entire functions
Journal of High Energy Physics, 2023 Recently a function was constructed that satisfies all known properties of a tree-level scattering of four massless scalars via the exchange of an infinite tower of particles with masses given by the non-trivial zeroes of the Riemann zeta function. A key
Claude Duhr, Chandrashekhar Kshirsagar
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On algebraic differential equations concerning the Riemann-zeta function and the Euler-gamma function [PDF]
Complex Variables and Elliptic Equations, 2020 In this paper, we prove that ζ is not a solution of any non-trivial algebraic differential equation whose coefficients are polynomials in over the ring of polynomials in , are nonnegative integers.
Qiongyan Wang, Z. Li, Man-Li Liu, Nan Li
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Lower bounds for discrete negative moments of the Riemann zeta function [PDF]
Algebra & Number Theory, 2020 We prove lower bounds for the discrete negative $2k$th moment of the derivative of the Riemann zeta function for all fractional $k\geqslant 0$. The bounds are in line with a conjecture of Gonek and Hejhal.
W. Heap, Junxian Li, J. Zhao
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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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Extreme values of the Riemann zeta function and its argument [PDF]
Mathematische Annalen, 2017 We combine our version of the resonance method with certain convolution formulas for ζ(s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
A. Bondarenko, K. Seip
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SHARP UPPER BOUNDS FOR FRACTIONAL MOMENTS OF THE RIEMANN ZETA FUNCTION [PDF]
Quarterly Journal of Mathematics, 2019 We establish sharp upper bounds for the $2k$th moment of the Riemann zeta function on the critical line, for all real $0 \leqslant k \leqslant 2$. This improves on earlier work of Ramachandra, Heath-Brown and Bettin–Chandee–Radziwiłł.
W. Heap +2 more
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