Results 21 to 30 of about 17,792 (168)
An arithmetical mapping and applications to Ω-results for the Riemann zeta function [PDF]
Acta Arithmetica, 2009 In this paper we study the linear mapping that sends a sequence (an) to (bn) where bn = ∑ d|n d −αan/d. We investigate for which values of α this is a bounded operator from l to l and show the operator norm is closely connected to the Riemann zeta function.
Titus Hilberdink
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Arithmetic calculus of Fourier transforms by Igusa local zeta functions [PDF]
Transactions of the American Mathematical Society, 1994 We show the possibility of explicit calculation of the Fourier transforms of complex powers of relative invariants of some prehomogeneous vector spaces over R \mathbb {R} by using the explicit form of p p -adic Igusa local zeta functions.
Tatsuo Kimura
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Universality theorems of the Selberg zeta functions for arithmetic groups
, 2023 20 ...
Yasufumi Hashimoto
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On the Nature of γ-th Arithmetic Zeta Functions [PDF]
Symmetry, 2020 Symmetry and elementary symmetric functions are main components of the proof of the celebrated Hermite–Lindemann theorem (about the transcendence of e α , for algebraic values of α ) which settled the ancient Greek problem of squaring the circle. In this paper, we are interested in similar results, but for powers such as e γ log n
Pavel Trojovský
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Arithmetic expressions of Selberg's zeta functions for congruence subgroups
Journal of Number Theory, 2004 12 ...
Yasufumi Hashimoto
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An arithmetic zeta function respecting multiplicities
, 2020 In this paper, we study the arithmetic zeta function $$\mathscr{Z}_{\mathcal{X}}(s) = \prod_p \prod_{\substack{x \in \mathcal{X}_p \\ \text{closed}}} \Big( \frac{1}{1-|κ(x)|^{-s}} \Big)^{\mathfrak{m}_{p}(x)}$$ associated to a scheme $\mathcal{X}$ of finite type over $\mathbb{Z}$, where $κ(x)$ denotes the residue field and $\mathfrak{m}_{p}(x)$ the ...
Lukas Prader
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Equalities, congruences, and quotients of zeta functions in Arithmetic Mirror Symmetry
, 2005 6 ...
C. Douglas Haessig
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Arithmetic equivalence for function fields, the Goss zeta function and a generalisation
Journal of Number Theory, 2009 A theorem of Tate and Turner says that global function fields have the same zeta function if and only if the Jacobians of the corresponding curves are isogenous. In this note, we investigate what happens if we replace the usual (characteristic zero) zeta function by the positive characteristic zeta function introduced by Goss.
Gunther Cornelissen +2 more
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Zeta Functions on Arithmetic Surfaces
, 2013 We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called mean-periodicity correspondence, which is comparable to the better known automorphicity conjectures for the ...
Thomas Oliver
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Weighted discrete universality of the Riemann zeta-function
Mathematical Modelling and Analysis, 2020 It is well known that the Riemann zeta-function is universal in the Voronin sense, i.e., its shifts ζ(s + iτ), τ ∈ R, approximate a wide class of analytic functions. The universality of ζ(s) is called discrete if τ take values from a certain discrete set.
Antanas Laurinčikas +2 more
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