Results 21 to 30 of about 71,062 (275)
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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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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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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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.
Winston Heap, Junxian Li, J. Zhao
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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 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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Decoupling, exponential sums and the Riemann zeta function [PDF]
, 2014 We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in [H].
J. Bourgain
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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.
Winston Heap +2 more
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Riemann’s zeta function and beyond [PDF]
Bulletin of the American Mathematical Society, 2003 In recent yearsLL-functions and their analytic properties have assumed a central role in number theory and automorphic forms. In this expository article, we describe the two major methods for proving the analytic continuation and functional equations ofLL-functions: the method of integral representations, and the method of Fourier expansions of ...
Stephen Gelbart, Stephen D. Miller
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Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function [PDF]
Journal of the London Mathematical Society, 2020 We consider partial sums of a weighted Steinhaus random multiplicative function and view this as a model for the Riemann zeta function. We give a description of the tails and high moments of this object.
Marco Aymone, Winston Heap, J. Zhao
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