Results 111 to 120 of about 552,780 (265)
A Proof of Riemann Hypothesis [PDF]
arXiv, 2019 The meromorphic function $W(s)$ introduced in the Riemann-Zeta function $\zeta(s) = W(s) \zeta(1-s)$ maps the line of $s = 1/2 + it$ onto the unit circle in $W$-space. $|W(s)| = 0$ gives the trivial zeroes of the Riemann-Zeta function $\zeta(s)$. In the range: $0 < |W(s)| \neq 1$, $\zeta(s)$ does not have nontrivial zeroes.
arxiv
Sonification of the Riemann Zeta Function [PDF]
Proceedings of the 25th International Conference on Auditory Display (ICAD 2019), 2019 The Riemann zeta function is one of the great wonders of mathematics, with a deep and still not fully solved connection to the prime numbers. It is defined via an infinite sum analogous to Fourier additive synthesis, and can be calculated in various ways.
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Symmetries and the Riemann Hypothesis [PDF]
arXiv, 2008 Associated to classical semi-simple groups and their maximal parabolics are genuine zeta functions. Naturally related to Riemann's zeta and governed by symmetries, including that of Weyl, these zetas are expected to satisfy the Riemann hypothesis.
arxiv
The inverse Riemann zeta function
, 2021 In this article, we develop a formula for an inverse Riemann zeta function such that for $w=ζ(s)$ we have $s=ζ^{-1}(w)$ for real and complex domains $s$ and $w$. The presented work is based on extending the analytical recurrence formulas for trivial and non-trivial zeros as to solve an equation $ζ(s)-w=0$ for a given $w$-domain using logarithmic ...
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A Connection between the Riemann Hypothesis and Uniqueness of the Riemann zeta function [PDF]
arXiv, 2016 In this paper, we give a connection between the Riemann hypothesis and uniqueness of the Riemann zeta function and an analogue for L-functions.
arxiv
Characteristic polynomials, spectral-based Riemann-Zeta functions and entropy indices of n-dimensional hypercubes. [PDF]
J Math Chem, 2023 Balasubramanian K.
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The Generalized Riemann Zeta Functions and their Applications in the Calculations of Neutron Cross Sections [PDF]
, 1965 J. W. W., M. Atoji, F. L. Clark
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Separation of zeros of the Riemann zeta-function [PDF]
, 1966 Robert S. Lehman
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Renormdynamics, multiparticle production, negative binomial distribution and Riemann zeta function [PDF]
arXiv, 2010 Renormdynamic equations of motion and their solutions are given. New equation for NBD distribution and Riemann zeta function invented. Explicit forms of the z-Scaling functions are constructed.
arxiv