Results 241 to 250 of about 5,895,830 (271)
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Identities Related to the Riemann Zeta Function and Periodic Zeta Functions
2013Several interesting entries from page 196 in the lost notebook are examined. These relate to two of Ramanujan’s papers on integrals.
George E. Andrews, Bruce C. Berndt
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Sum of the periodic zeta-function over the nontrivial zeros of the Riemann zeta-function [PDF]
Analysis (Germany), 2008 The periodic zeta-function in the title is the analytic continuation into the entire \(s\)-plane of the Dirichlet series \[ L(s,k/l)= \sum^\infty_{n=1} e^{2\pi ink/l} n^{-s}, \] where \(k\) and \(l\) are coprime positive integers with \(k< l\). If \(\rho= \beta+ i\gamma\) denotes a typical nontrivial zero of the Riemann zeta function, \textit{J ...
Ramunas Garunkštis
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Universality theorems for zeta-functions with periodic coefficients
Siberian Mathematical Journal, 2016 In a series of works by the author (see for instance [Acta Appl. Math. 78, No. 1--3, 251--271 (2003; Zbl 1038.11059); Izv. Math. 74, No. 3, 515--539 (2010); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 74, No. 3, 79--102 (2010; Zbl 1200.11067)]), the universality in Voronin's sense for the certain zeta-functions with periodic coefficients are ...
A Laurincikas
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Remarks on the universality of the periodic zeta function
Mathematical Notes, 2006In the paper, the universality of a zeta-function \[ \zeta(s,\mathfrak A)=\sum_{m=1}^\infty a_m m^{-s}, \quad \Re s>1, \] where \(\mathfrak A=\{a_m:m\in\mathbb N\}\) is a periodic sequence of complex numbers with the least period \(k\in\mathbb N\), is considered. The authors continue the investigations of \textit{J.~Steuding} [Value-distribution of \(L\
A Laurincikas
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Zeta Functions and Periodic Orbit Theory: A Review
Results in Mathematics, 1993This is a comprehensive review of recent work on zeta functions, periodic orbit theory and their interrelations with the Selberg trace formula. Work on the quantization of chaos is also surveyed. The emphasis is on Lie group representation theory and differential geometry. Connections to string theory are also discussed. The following sample of section
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PERIOD DEFORMATIONS OF MULTIPLE HURWITZ ZETA FUNCTIONS
International Journal of Mathematics, 2007We study continuous period deformations of the multiple Hurwitz zeta functions and their derivatives. Moreover we investigate period deformations of the generalized multiple gamma and sine functions and give applications.
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The joint distribution of periodic zeta-functions
Studia Scientiarum Mathematicarum Hungarica, 2011In this paper, the joint approximation of a given collection of analytic functions by a collection of shifts of zeta-functions with periodic coefficients is obtained. This is applied to prove the functional independence for these zeta-functions.
Roma kačinskaitė, Antanas Laurinčikas
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The Atkinson formula for the periodic zeta-function
Lithuanian Mathematical Journal, 2007We give an Atkinson-type formula for the periodic zeta-function ζλ with rational parameter λ.
J. Karaliūnaitė, A. Laurinčikas
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On discrete universality of the periodic zeta-function
2006In the paper, the discrete universality of the periodic zeta-function is considered. For this, a discrete limit theorem in the sense of the weak convergence of probability measures in the space of analytic functions is applied.
Javtokas, Algirdas +2 more
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Joint Universality of Zeta Functions with Periodic Coefficients. II
Siberian Mathematical Journal, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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