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We show that any dominant meromorphic self‐map f:X→X of a compact Kähler manifold X is an Artin–Mazur map. More precisely, if Pn(f) is the number of its isolated periodic points of period n (counted with multiplicity), then Pn(f) grows at most exponentially fast with respect to n and the...
Let H2 denote the Hardy space of Dirichlet series f(s)=∑n⩾1ann−s with square summable coefficients and suppose that φ is a symbol generating a composition operator on H2 by Cφ(f)=f∘φ. Let ζ denote the Riemann zeta function and α0=1.48… the unique positive solution of the equation αζ(1+α)=2. We...
Given an infinite set of special divisors satisfying a mild regularity condition, we prove the existence of a Borcherds product of non‐zero weight whose divisor is supported on these special divisors. We also show that every meromorphic Borcherds product is the quotient of two holomorphic ones....
In this short note we prove that the reduced group C*‐algebra of a locally compact group admits a non‐zero trace if and only if the amenable radical of the group is open. This completely answers a question raised by Forrest, Spronk and Wiersma.
We affirmatively answer a question of Erdős and Pach from 1983 by showing the following: there is some constant C>0 such that for any graph G on Cklnk vertices either G or its complement G¯ has an induced subgraph on k vertices with minimum degree at least 12(k−1).
We give an intrinsic (coordinate‐free) construction of the tangent groupoid of a filtered manifold. This is an analogue of Connes' tangent groupoid which is pertinent for the analysis of certain subelliptic differential operators. It is a deformation of the pair groupoid to a bundle of nilpotent...
A spectral sequence is defined which converges to the Čech cohomology of the Euclidean hull of a tiling of the plane with Euclidean finite local complexity. The terms of the second page are determined by the so‐called Euclidean pattern‐equivariant (ePE) homology and ePE cohomology groups of the...
An equational condition is a set of equations in an algebraic language, and an algebraic structure satisfies such a condition if it possesses terms that meet the required equations. We find a single nontrivial equational condition which is implied by any nontrivial idempotent equational condition.
We show that the simple elements of the dual Garside structure of an Artin group of type Dn are Mikado braids, giving a positive answer to a conjecture of Digne and the second author. To this end, we use an embedding of the Artin group of type Dn in a suitable quotient of an Artin group of type...
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