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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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Riemann surface of the Riemann zeta function

Journal of Mathematical Analysis and Applications
In this paper we treat the classical Riemann zeta function as a function of three variables: one is the usual complex $\adyn$-dimensional, customly denoted as $s$, another two are complex infinite dimensional, we denote it as $\b = \{b_n\}_{n=1}^{\infty}$ and $\z =\{z_n\}_{n=1}^{\infty}$. When $\b = \{1\}_{n=1}^{\infty}$ and $\z = \{\frac{1}{n}\}_{n=1}^
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A Bicomplex Riemann Zeta Function

Tokyo Journal of Mathematics, 2004
The author uses a commutative generalization of complex numbers, called bicomplex numbers, to introduce a holomorphic Riemann zeta function of two complex variables, which satisfies the complexified Cauchy-Riemann equations. Moreover, the author establishes a bicomplex Riemann hypothesis which is equivalent to the complex Riemann hypothesis of one ...
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Fourier coefficients associated with the Riemann zeta-function

Karpatsʹkì Matematičnì Publìkacìï, 2016
We study the Riemann zeta-function $\zeta(s)$ by a Fourier series method. The summation of $\log|\zeta(s)|$ with the kernel $1/|s|^{6}$ on the critical line $\mathrm{Re}\; s = \frac{1}{2}$ is the main result of our investigation.
Yu.V. Basiuk, S.I. Tarasyuk
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Riemann's Prime Counting Function and Riemann Zeta Function

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Genus two KdV soliton gases and their long-time asymptotics

Forum of Mathematics, Sigma
This paper employs the Riemann-Hilbert problem and nonlinear steepest descent method of Deift-Zhou to provide a comprehensive analysis of the asymptotic behavior of the genus two Korteweg-de Vries soliton gases.
Deng-Shan Wang, Dinghao Zhu, Xiaodong Zhu   +2 more
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Estimates of Upper Bound for a Function Associated with Riemann-Liouville Fractional Integral via h-Convex Functions

Journal of Function Spaces, 2019
A new identity involving Riemann-Liouville fractional integral is proposed. The result is then used to obtain some estimates of upper bound for a function associated with Riemann-Liouville fractional integral via h-convex functions.
Shan-He Wu, Muhammad Uzair Awan
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Riemann–Liouville Fractional Calculus of Nonlinear Hidden Variable Recurrent Fractal Interpolation Functions Based on Rakotch Contraction

Journal of Function Spaces
In this paper, we study Riemann–Liouville fractional calculus of nonlinear hidden variable recurrent fractal interpolation function (HVRFIF) constructed based on Rakotch contraction, which is a generalization of Banach contraction.
Chung-Il Ro, Chol-Hui Yun, Song-Chol Kwon, Un-Ryong Rim   +3 more
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Inequalities for Riemann’s zeta function

Portugaliae Mathematica, 2009
Let ζ and Λ be the Riemann zeta function and the von Mangoldt function, respectively. Further, let c > 0
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Long-time asymptotic behavior for the Hermitian symmetric space derivative nonlinear Schrödinger equation

Advanced Nonlinear Studies
Resorting to the spectral analysis of the 4 × 4 matrix spectral problem, we construct a 4 × 4 matrix Riemann–Hilbert problem to solve the initial value problem for the Hermitian symmetric space derivative nonlinear Schrödinger equation.
Chen Mingming, Geng Xianguo, Liu Huan
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