Results 41 to 50 of about 17,792 (168)

Integral formulae of arithmetical characteristics relating to the zeta-function of Hurwitz

Publicationes Mathematicae Debrecen, 2022
Folgende Formel \[ \int_0^1 \zeta(1-s,w_1)\zeta(1-s, w_2)\,du = 2 \Gamma(s)^2 \frac{\zeta(2s)}{(2\pi)^{2s}} \frac{(k,l)}{[k,l]}, \] abgeleitet aus der Fourierentwicklung \(\zeta(1-s, \omega)\cdot (2\pi)^s/2 \Gamma(s)\), für \(w_1= ku - [ku]\), \(w_2 = lu- [lu]\) \((k,l\) natürliche Zahlen, \((k,l)\) ihr g.g.T., \([k,l]\) ihr k.g.V.) bildet das ...
Miklós Mikolás
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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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Zeta functions and composition factors for arithmetic orders

Mathematische Zeitschrift, 1987
In earlier papers, the present authors have made a deep study of ''zeta- functions'' associated with the counting of left ideals X in an arithmetic order \(\Lambda\) according to the index (\(\Lambda\) :X) of X in \(\Lambda\) ; see their survey article [Lect. Notes Math. 1142, 50-87 (1985; Zbl 0575.12007)]. Here \(\Lambda\) is a \({\mathbb{Z}}\)-order (
Bushnell, Colin J., Reiner, Irving
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Multiple finite Riemann zeta functions

, 2004
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then, describe the ...
Kimoto, K., Kurokawa, N., Matsumoto, S., Wakayama, M.   +3 more
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Igusa’s Local Zeta Functions and Exponential Sums for Arithmetically Non Degenerate Polynomials [PDF]

Journal de Théorie des Nombres de Bordeaux, 2018
We study the twisted local zeta function associated to a polynomial in two variables with coefficients in a non-Archimedean local field of arbitrary characteristic. Under the hypothesis that the polynomial is arithmetically non degenerate, we obtain an explicit list of candidates for the poles in terms of geometric data obtained from a family of ...
Adriana A. Albarracin-Mantilla, Edwin León-Cardenal   +1 more
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Truncated Infinitesimal Shifts, Spectral Operators and Quantized Universality of the Riemann Zeta Function [PDF]

, 2013
We survey some of the universality properties of the Riemann zeta function $\zeta(s)$ and then explain how to obtain a natural quantization of Voronin's universality theorem (and of its various extensions).
Herichi, Hafedh, Lapidus, Michel L.
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Mean-square values of the Riemann zeta function on arithmetic progressions

Monatshefte für Mathematik
Comment: This is an updated version of arXiv:2212.06520.
Hirotaka Kobayashi
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Hankel determinants of zeta values [PDF]

, 2015
We study the asymptotics of Hankel determinants constructed using the values ς(an + b) of the Riemann zeta function at positive integers in an arithmetic progression.
Haynes, Alan, Zudilin, Wadim
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Modular Calabi-Yau fourfolds and connections to M-theory fluxes

Journal of High Energy Physics
In this work, we study the local zeta functions of Calabi-Yau fourfolds. This is done by developing arithmetic deformation techniques to compute the factor of the zeta function that is attributed to the horizontal four-form cohomology.
Hans Jockers, Sören Kotlewski, Pyry Kuusela   +2 more
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Geometry of the arithmetic site [PDF]

, 2015
We introduce the Arithmetic Site: an algebraic geometric space deeply related to the non-commutative geometric approach to the Riemann Hypothesis. We prove that the non-commutative space quotient of the adele class space of the field of rational numbers ...
Connes, Alain, Consani, Caterina
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