Zeta functions
Multifractal zeta functions
... Artin-Mazur zeta-functions in number theory and the use of the Ruelle zeta-functions in dynamical systems, Lapidus and collaborators (see books by Lapidus & van Frankenhuysen [32, 33] and ...
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Zeta functions in triangulated categories
... answer to that question would have quite interesting corollaries when applying to zeta functions in the triangulated category of motives over a field. Below we will show an existence of two opposite special ...
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A converse theorem for double Dirichlet series and Shintani zeta functions
... Shintani’s zeta functions [13] have been studied extensively because of their arithmetic na- ture and because they are important examples of zeta functions associated to prehomogenuous vector ...
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The Ruelle operator, zeta functions and the asymptotic distribution of closed orbits
... next study geodesic flows on surfaces of constant negative curvature. We compare the zeta functions of a geodesic flow and a certain suspension flow. These results are then used to recover asymptotic ...
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Hyperbolic systems, zeta functions and other friends
... Returning to the definition of zeta functions for flows, we can consider a simple ex- ample which illustrates how things work, before giving the definition in the general case. Example 1.6 (Suspension flow) ...
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Time-changes preserving zeta functions
... dynamical zeta functions. Thus, for example, the space of all zeta functions is closed under multiplication, because the sum of two realizable sequences is realizable, and is closed under a ...
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Multifractal spectra and multifractal zeta functions
... these zeta-functions will provide explicit formulas for the “counting function” N μ,δ (α; r) allowing us to express N μ,δ (α; r) as a sum involving the residues of these zeta-functions; this ...
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Mixed Zeta Functions
... weighting functions, provided an associated multivariable Dirichlet series K has good properties (see ...mixed zeta functions extend to meromorphic functions on C or some halfplane C >κ , ...
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Discrete limit theorems for Estermann zeta-functions. II
... convergence of probability measures in the space of meromorphic functions for the Estermann zeta-function with explicitly given the limit measure is proved.. 2000 Mathematics Subject Cla[r] ...
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Discrete limit theorems for Estermann zeta-functions. I
... The function E(s; k l , α) with parameter α = 0 was introduced by T. Estermann in [2] for needs of the representation of a number as the sum of two products. I. Kiuchi investigated [6] E(s; k l , α) for α ∈ ( − 1, 0]. ...
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Special Values of Zeta-Functions for Proper Regular Arithmetic Surfaces
... Meanwhile Flach and Morin gave conjectural descriptions of the special values of arithmetic ζ-functions ζpX , sq associated to any proper regular arithmetic scheme X Ñ Spec Z in [8]. They proved that under certain ...
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Fundamental Domains of Gamma and Zeta Functions
... Riemann Zeta function is one of the most studied transcendental functions, in view of its many applications in number theory, algebra, complex analysis, and statistics as well as in ...of Zeta ...
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On zeta functions and Anosov diffeomorphisms
... However, few examples of Anosov diffeomorphisms are known and these only on tori and nilmanifolds and manifolds finitely covered by them - the so.called hyperbolic toral automorphisms an[r] ...
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Two double inequalities for k gamma and k Riemann zeta functions
... 3. Nguyen, VV, Ngo, PNN: An inequality for the gamma function. Int. Math. Forum 4(28), 1379-1382 (2009) 4. Díaz, R, Pariguan, E: On hypergeometric functions and Pochhammer k-symbol. Divulg. Mat. 15(2), 179-192 ...
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Ted Chinburg, Professor of Mathematics Supervisor of Dissertation David Harbater, Professor of Mathematics Graduate Group Chairperson Dissertation Committee: Ted Chinburg, Professor of Mathematics Philip Gressman, Associate Professor of Mathematics Robert Strain, Associate Professor of Mathematics
... distance zeta functions where the summation is over n-tuples of positive integers, and gives expressions for the residues of its poles, all of which are ...
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The Riemann Hypothesis Millennium Prize Problem
... Riemann’s zeta function is the most important subject of study and has a plenty of interesting ...of zeta functions in the Number Theory is very significant, and is connected to various fundamental ...
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Analytic number theory in India during 2001 2010
... most functions that are commonly called L- functions or zeta ...two functions F 6= G in the Selberg class with degF ≥ degG, and shows that for T sufficiently large, there is a zero ρ = β + iγ ...
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A master integral in four parameters
... In this paper we consider a master integral in four arbitrary parameters. The integrand involves the logarithmic function and the Gauss hypergeomet- ric function, which in certain special cases the integral reduces to ...
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The Towering Zeta Function
... Remark 2: The arguments that lead to roots have singular solutions to the inverse zeta functions of roots that generate them in the backward direction. This points to the fact that a root can only be ...
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Riemann Hypothesis
... modifying zeta functions. The properties of zeta functions are studied; these properties lead to new regularities of zeta ...ified zeta functions allows estimating the ...
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