Results 31 to 40 of about 545,098 (196)
WSEAS TRANSACTIONS ON MATHEMATICS, 2020 In this work we are interested by cotangent sum related to Estermann zeta function in rational arguments. In the first place we look at the maximum and the moment as they did H. Maier and M. Th. Rassias in short interval and get some interesting new identities. Afterwards, based on some recent results, we study special cases where we provide the series
Mouloud Goubi
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A mean-square value of the Riemann zeta function over an arithmetic progression
, 2022 We obtain an asymptotic formula for the second discrete moment of the Riemann zeta function over the arithmetic progression $\frac{1}{2} + in$. It shows that the first main term is equal to that of the continuous mean value.
Hirotaka Kobayashi
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Some arithmetic properties of partial zeta functions weighted by a sign character
Journal of Number Theory, 2010 AbstractWe introduce two types of zeta functions (Ψ-type and ζ-type) of one complex variable associated to an arbitrary number field K. We prove various arithmetic identities which involve both of them. We also study their special values at integral arguments.
Hugo Chapdelaine
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Riemann zeta function and arithmetic progression of higher order [PDF]
Notes on Number Theory and Discrete Mathematics, 2020 Éder Furtado +2 more
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``Quasi''-norm of an arithmetical convolution operator and the order of the Riemann zeta function [PDF]
Functiones et Approximatio Commentarii Mathematici, 2013 In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = ni® for its connection to the Riemann zeta function on the line
Titus Hilberdink
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Mean-square values of the Riemann zeta function on arithmetic progressions
Monatshefte für MathematikComment: This is an updated version of arXiv:2212.06520.
Hirotaka Kobayashi
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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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On Discrete Approximation of Analytic Functions by Shifts of the Lerch Zeta Function
Mathematics, 2022 The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider the approximation of analytic functions by discrete shifts of the Lerch zeta function, and we prove that, for arbitrary parameters and a
Audronė Rimkevičienė +1 more
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Unified Theory of Zeta-Functions Allied to Epstein Zeta-Functions and Associated with Maass Forms
Mathematics, 2023 In this paper, we shall establish a hierarchy of functional equations (as a G-function hierarchy) by unifying zeta-functions that satisfy the Hecke functional equation and those corresponding to Maass forms in the framework of the ramified functional ...
Nianliang Wang +2 more
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Poincar�� series of Lie lattices and representation zeta functions of arithmetic groups
, 2017 We compute explicit formulae for Dirichlet generating functions enumerating finite-dimensional irreducible complex representations of potent and saturable principal congruence subgroups of $\mathrm{SL}_4^m(\mathfrak{o})$ ($m\in\mathbb{N}$) for $\mathfrak{o}$ a compact DVR of characteristic $0$ and odd residue field characteristic.
Michele Zordan
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