Artin formalism for Selberg zeta functions of co-finite Kleinian groups

Eliot Brenner; Florin Spinu

Displaying similar documents to “Artin formalism for Selberg zeta functions of co-finite Kleinian groups”

Weyl type upper bounds on the number of resonances near the real axis for trapped systems

Plamen Stefanov (2001)

Journées équations aux dérivées partielles

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We study semiclassical resonances in a box $Ω (h)$ of height $h^{N}$ , $N ≫ 1$ . We show that the semiclassical wave front set of the resonant states (including the “generalized eigenfunctions”) is contained in the set $𝒯$ of the trapped bicharacteristics. We also show that for a suitable self-adjoint reference operator $P^{#} (h)$ with discrete spectrum the number of resonances in $Ω (h)$ is bounded by the number of eigenvalues of $P^{#} (h)$ in an interval a bit larger than the projection of $Ω (h)$ on the real line. As an application,...

Characterizations of groups generated by Kronecker sets

András Biró (2007)

Journal de Théorie des Nombres de Bordeaux

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In recent years, starting with the paper [B-D-S], we have investigated the possibility of characterizing countable subgroups of the torus $T = R / Z$ by subsets of $Z$ . Here we consider new types of subgroups: let $K \subseteq T$ be a Kronecker set (a compact set on which every continuous function $f : K \to T$ can be uniformly approximated by characters of $T$ ), and $G$ the group generated by $K$ . We prove (Theorem 1) that $G$ can be characterized by a subset of $Z^{2}$ (instead of a subset of $Z$ ). If $K$ is finite, Theorem 1 implies our...

On the mean square of the divisor function in short intervals

Aleksandar Ivić (2009)

Journal de Théorie des Nombres de Bordeaux

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We provide upper bounds for the mean square integral $\int_{X}^{2 X} {(𝔻_{k} (x + h) - 𝔻_{k} (x))}^{2} d x,$ where $h = h (X) ≫ 1, h = o (x) as X \to \infty$ and $h$ lies in a suitable range. For $k \geq 2$ a fixed integer, $𝔻_{k} (x)$ is the error term in the asymptotic formula for the summatory function of the divisor function $d_{k} (n)$ , generated by $ζ^{k} (s)$ .

The Reidemeister zeta function and the computation of the Nielsen zeta function

A. Fel'shtyn (1991)

Colloquium Mathematicum

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On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator $W_{k} : = Δ + \frac{k}{x_{n}} \frac{\partial}{\partial x_{n}}$ on $ℝ^{n}$ is proved. In this note there is shown that in the cases $k \neq 0$ , $k \neq 2$ no other transforms of this kind exist and for case $k = 2$ , all such transforms are described.