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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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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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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A Tapestry of Ideas with Ramanujan’s Formula Woven In
AxiomsZeta-functions play a fundamental role in many fields where there is a norm or a means to measure distance. They are usually given in the forms of Dirichlet series (additive), and they sometimes possess the Euler product (multiplicative) when the domain ...
Nianliang Wang +2 more
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Integral Transforms in Number Theory
AxiomsIntegral transforms play a fundamental role in science and engineering. Above all, the Fourier transform is the most vital, which has some specifications—Laplace transform, Mellin transform, etc., with their inverse transforms. In this paper, we restrict
Guodong Liu +2 more
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Asymptotics of the Determinant of Discrete Laplacians on Triangulated and Quadrangulated Surfaces. [PDF]
Commun Math Phys, 2022 Izyurov K, Khristoforov M.
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Stieltjes constants of L-functions in the extended Selberg class. [PDF]
Ramanujan J, 2021 Inoue S, Eddin SS, Suriajaya AI.
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Definite orthogonal modular forms: computations, excursions, and discoveries. [PDF]
Res Number Theory, 2022 Assaf E +5 more
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The nature of π-hole interactions between iodide anions and quinoid rings in the crystalline state. [PDF]
IUCrJ, 2023 Milašinović V +5 more
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Understanding Harmonic Structures Through Instantaneous Frequency. [PDF]
IEEE Open J Signal Process, 2022 Fabus MS +3 more
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