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A UNIFIED METHOD FOR EVALUATING RIEMANN ZETA FUNCTIONS, DIRICHLET SERIES, ASSOCIATED CLAUSEN FUNCTIONS, OTHER ALLIED SERIES, AND NEW CLASSES OF INFINITE SERIES [PDF]
International Journal of Pure and Apllied Mathematics, 2014 Abstract: We have shown here for the first time that the completeness relation provides a simple unified theoretical framework for deriving different kinds of new recurrence formulae for Riemann Zeta Functions, Dirichlet series and Other Allied Series by selecting only different forms of complete set of orthonormal function (CSOF) in contrast to the ...
K.A. Acharya, K.J. Tej, A.K. Samanta
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On the Epstein zeta function and the Zeros of a Class of Dirichlet series [PDF]
Journal of Mathematical Analysis and Applications, 2021 By generalizing the classical Selberg-Chowla formula, we establish the analytic continuation and functional equation for a large class of Epstein zeta functions.
P. Ribeiro, S. Yakubovich
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Zeta-regularization of arithmetic sequences [PDF]
EPJ Web of Conferences, 2020 Is it possible to give a reasonable value to the infinite product 1 × 2 × 3 × · · · × n × · · · ? In other words, can we define some sort of convergence of the finite product 1 × 2 × 3 × · · · × n when n goes to infinity?
Allouche Jean-Paul
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Mathematical Modelling and Analysis, 2023 In the paper, we construct an absolutely convergent Dirichlet series which in the mean is close to the periodic Hurwitz zeta-function, and has the universality property on the approximation of a wide class of analytic functions.
A. Balčiūnas +2 more
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On the meromorphic continuation of Beatty Zeta-functions and Sturmian Dirichlet series [PDF]
Journal of Number Theory, 2018 For a positive irrational number α, we study the ordinary Dirichlet series ζ α ( s ) = ∑ n ≥ 1 ⌊ α n ⌋ − s and S α ( s ) = ∑ n ≥ 1 ( ⌈ α n ⌉ − ⌈ α ( n − 1 ) ⌉ ) n − s .
Athanasios Sourmelidis
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Some remarks on the mean value of the Riemann zetafunction and other Dirichlet series. III [PDF]
Annales Academiae Scientiarum Fennicae Series A I Mathematica, 1980 This is a sequel (Part II) to an earlier article with the same title. There are reasons to expect that the estimates proved in Part I without the factor $(\log\log H)^{-C}$ represent the real truth, and this is indeed proved in part II on the assumption that in the first estimate $2k$ is an integer.
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Multiple Dirichlet Series and Moments of Zeta and L-Functions [PDF]
Compositio Mathematica, 2001 This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic continuation and ...
A. Diaconu, D. Goldfeld, J. Hoffstein
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Ideal growth in amalgamated powers of nilpotent rings of class two and zeta functions of quiver representations [PDF]
Bulletin of the London Mathematical Society, 2022 Let L$L$ be a nilpotent algebra of class two over a compact discrete valuation ring A$A$ of characteristic zero or of sufficiently large positive characteristic. Let q$q$ be the residue cardinality of A$A$ . The ideal zeta function of L$L$ is a Dirichlet
T. Bauer, Michael M. Schein
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Discrete Approximation by a Dirichlet Series Connected to the Riemann Zeta-Function
, 2021 In the paper, a Dirichlet series ζuN(s) whose shifts ζuN(s+ikh), k=0,1,⋯, h>0, approximate analytic non-vanishing functions defined on the right-hand side of the critical strip is considered. This series is closely connected to the Riemann zeta-function.
A. Laurinčikas, D. Šiaučiūnas
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On the Mishou Theorem for Zeta-Functions with Periodic Coefficients
Mathematics, 2023 Let a={am} and b={bm} be two periodic sequences of complex numbers, and, additionally, a is multiplicative. In this paper, the joint approximation of a pair of analytic functions by shifts (ζnT(s+iτ;a),ζnT(s+iτ,α;b)) of absolutely convergent Dirichlet ...
A. Balčiūnas +3 more
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