The zeta function
Rational approximations to the zeta function
... The finite-dimensional operators described here have several advantages. • The determinants yield approximations to the zeta function itself (not just eigenvalues that correspond to zeros). • Having ...
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New series involving the zeta function
... Abstract. We evaluate sums of certain classes of new series involving the Riemann zeta function by using the theory of the double gamma function and a property of the gamma function. Relevant ...
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The Towering Zeta Function
... 9. Discussion of the Result The convergence of Power towers relates the vanishing of the zeta function to the half-line. This relationship comes from the property of complex power towers of the ...
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Moments of the Dedekind zeta function
... where G is the Barnes G-function which satisfies G(1) = 1 and G(z + 1) = Γ(z)G(z). Their formula actually allows for k to range continuously through values > −1/2 if we replace k 2 ! by Γ(k 2 + 1) and d k (p m ) ...
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Graph Zeta Function and Gauge Theories
... We raised the objection in the previous section, after leaving the comfortable terrain of ADE-quivers, that an immediate trouble with the zoo of quivers arising from general Yang-Mills or Chern-Simons theories is the ...
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Key Words: Riemann zeta function, xi function, zeta zeros, periods, critical line, Hilbert-Polya conjecture
... A program was written in MATLAB using the methods of Godfrey [10] for both the ζ-function and the complex Γ-function They are available in Godfrey’s MATLAB suite as part of the zeta-function ...
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The Inconsistency Problem of Riemann Zeta Function Equation
... The Riemann hypothesis is proved to be meaningless, which is unexpected by most people. The problem lied in Riemann's original paper of 1859. In the Riemann’s deduction, two formulas were improperly used without ...
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CiteSeerX — Zeta function regularization in de Sitter space:
... Abstract: We study an integral representation for the zeta function of the one-loop effective potential for a min- imally coupled massive scalar field in D-dimensional de Sitter spacetime. By deforming the ...
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CiteSeerX — Zeta-function Regularization, the Multiplicative Anomaly and the Wodzicki Residue
... the zeta-function regularized determinant is computed for the Laplace-type operators L 1 = −∆ + V 1 and L 2 = −∆ + V 2 , with V 1 , V 2 constant, in a D-dimensional compact smooth manifold M D , making use ...
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The dynamical zeta function for commuting automorphisms of zero dimensional groups
... dynamical zeta function for group actions, motivated by the classical dynamical zeta function of a single ...dynamical zeta function is established that highlights a crucial link ...
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The Riemann zeta function
... Reyes, Ernesto Oscar, "The Riemann zeta function" (2004). Theses Digitization Project. 2648. https://scholarworks.lib.csusb.edu/etd-project/2648 This Thesis is brought to you for free and open access by the ...
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Certain relationships among polygamma functions, Riemann zeta function and generalized zeta function
... Here, we aim at presenting cer- tain (presumably) new and (potentially) useful relationships among polygamma functions, Riemann zeta function, and generalized zeta function by mainly mod[r] ...
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Zeros of the Dedekind Zeta-Function
... as T → ∞. We will prove an analogue of this theorem for the zeros of the Dedekind zeta-function. Originally Montgomery proved this theorem for α ∈ (0, 1) but it was later extended to α ∈ [0, 1] by Goldston ...
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q Riemann zeta function
... n=1 (q n(s−1) /[n] s ), 0 < q < 1, s ∈ C. In this paper, we give q-Bernoulli numbers which can be viewed as interpolation of the above q-analogue of Riemann zeta function at negative integers in the same ...
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Zeta function for Anosov Flows
... Dynamical zeta functions, by analogy with their more famous counterparts in number theory, are a useful tool to study certain types of dynamical ...Selberg zeta function have been well understood for ...
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A Note on Riemann Zeta Function
... Riemann Zeta Function is an essential special function in analytical number theory; its connection to the distribution of prime numbers was the motivation to expand its domain from real numbers to ...
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The inverses of tails of the Riemann zeta function
... Riemann zeta function ζ n (s) –1 for 0 < s < 1, and computed the values [A –1 n,s ] and [B –1 n,s ], hence the values of the inverses of tails of the Riemann zeta function [ 1–2 1 1–s ζ n (s) ...
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An integral involving the generalized zeta function
... The result finds application in calculating the numerical value of the derivative of the Riemann zeta function at the point -1, a quantity that arises in the evaluation of determinants o[r] ...
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On Maslanka's Representation for the Riemann Zeta Function
... Throughout, it shall be very important to bear in mind the simple estimate for the size of the Pochhammer polynomials contained in the following lemma already proved in 3 , Lemma 2... P[r] ...
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On a mollifier of the perturbed Riemann zeta function
... ON A MOLLIFIER OF THE PERTURBED RIEMANN ZETA-FUNCTION PATRICK K ¨ UHN, NICOLAS ROBLES, AND DIRK ZEINDLER Abstract. The mollification ζ(s) + ζ 0 (s) put forward by Feng is computed by analytic methods coming ...
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