Higher Derivatives of the Hurwitz Zeta Function [PDF]
, 2011 The Riemann zeta function ζ(s) is one of the most fundamental functions in number theory. Euler demonstrated that ζ(s) is closely connected to the prime numbers and Riemann gave proofs of the basic analytic properties of the zeta function.
Musser, Jason
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Derivatives of the Dedekind Zeta Function Attached to a Complex Quadratic Field Extention [PDF]
, 2010 The Riemann Zeta Function is a function of vital importance in the study of number theory and other branches of mathematics. This is primarily due to its intrinsic link with the prime numbers of the ring of integers.
Salazar, Nathan
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, 2007 This paper sketches a technique for improving the rate of convergence of a general oscillatory sequence, and then applies this series acceleration algorithm to the polylogarithm and the Hurwitz zeta function.
A. Jonquière +10 more
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Freezing Transition, Characteristic Polynomials of Random Matrices, and the Riemann Zeta-Function
, 2012 We argue that the freezing transition scenario, previously explored in the statistical mechanics of 1/f-noise random energy models, also determines the value distribution of the maximum of the modulus of the characteristic polynomials of large N x N ...
A. Laurincicas +6 more
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On p-Adic Sector of Adelic String
, 2009 We consider construction of Lagrangians which are candidates for p-adic sector of an adelic open scalar string. Such Lagrangians have their origin in Lagrangian for a single p-adic string and contain the Riemann zeta function with the d'Alembertian in ...
B. Dragovich +21 more
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Fractal Complex Dimensions, Riemann Hypothesis and Invertibility of the Spectral Operator [PDF]
, 2013 A spectral reformulation of the Riemann hypothesis was obtained in [LaMa2] by the second author and H. Maier in terms of an inverse spectral problem for fractal strings.
Herichi, Hafedh, Lapidus, Michel L.
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On some mean value results for the zeta-function in short intervals [PDF]
, 2013 Let $\Delta(x)$ denote the error term in the Dirichlet divisor problem, and let $E(T)$ denote the error term in the asymptotic formula for the mean square of $|\zeta(1/2+it)|$. If $E^*(t) := E(t) - 2\pi\Delta^*(t/(2\pi))$ with $\Delta^*(x) := -\Delta(x)
Ivić, Aleksandar
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Spectral spacing correlations for chaotic and disordered systems
, 2000 New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances.
Bohigas, O. +2 more
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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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Evanescent wave in multiple slit diffraction and n-array antennas in metamaterial using Cesàro convergence. [PDF]
Sci Rep, 2023 Nellambakam Y +2 more
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