Results 11 to 20 of about 75,204 (223)
Explicit zero density for the Riemann zeta function [PDF]
Journal of Mathematical Analysis and Applications, 2018 Let N ( σ , T ) denote the number of nontrivial zeros of the Riemann zeta function with real part greater than σ and imaginary part between 0 and T. We provide explicit upper bounds for N ( σ , T ) commonly referred to as a zero density result.
H. Kadiri, Allysa Lumley, Nathan Ng
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Aspects of the screw function corresponding to the Riemann zeta‐function [PDF]
Journal of the London Mathematical Society, 2022 We introduce a screw function corresponding to the Riemann zeta‐function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function.
Masatoshi Suzuki
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Four Variants of Riemann Zeta Function
Mathematics, 2022 By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in
Nadia N. Li, Wenchang Chu
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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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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 ...
Gelbart, Stephen S., Miller, Stephen D.
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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
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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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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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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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