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作者：Bary-Soroker, Lior; Koukoulopoulos, Dimitris; Kozma, Gady
作者单位：Tel Aviv University; Universite de Montreal; Weizmann Institute of Science
摘要：Let mu be a probability measure on Z that is not a Dirac mass and that has finite support. We prove that if the coefficients of a monic polynomial f (x) is an element of Z[x] of degree n are chosen independently at random according to mu while ensuring that f (0) not equal 0, then there is a positive constant theta = theta (mu) such that f (x) has no divisors of degree <= theta n with probability that tends to 1 as n -> infinity. Furthermore, in certain cases, we show that a random polynomial ...
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作者：De Filippis, Cristiana; Mingione, Giuseppe
作者单位：University of Parma
摘要：Local Schauder theory holds in the nonuniformly elliptic setting. Specifically, first derivatives of solutions to nonuniformly elliptic problems are locally Holder continuous if so are their coefficients.
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作者：Kim, Dongryul M.; Oh, Hee
作者单位：Yale University; Korea Institute for Advanced Study (KIAS)
摘要：Let Gamma < PSL2( C) similar or equal to Isom(+) (H-3) be a finitely generated non-Fuchsian Kleinian group whose ordinary set Omega = S-2 - Lambda has at least two components. Let rho : Gamma -> PSL2( C) be a faithful discrete non-Fuchsian representation with boundary map f : Lambda -> S-2 on the limit set. In this paper, we obtain a new rigidity theorem: if f is conformal on Lambda, in the sense that f maps every circular slice of Lambda into a circle, then f extends to a Mobius transformatio...
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作者：Canzani, Yaiza; Galkowski, Jeffrey
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of London; University College London
摘要：We obtain new quantitative estimates on Weyl Law remainders under dynamical assumptions on the geodesic flow. On a smooth compact Riemannian manifold (M, g) of dimension n, let H(lambda )denote the kernel of the spectral projector for the Laplacian, (1)[0,lambda(2)](-delta(g)). Assuming only that the set of near periodic geodesics over W subset of M has small measure, we prove that as lambda -> infinity integral(W) Pi(lambda) (x, x)dx = (2 pi)(-n) vol(R)(n)(B) volg(W) lambda(n) + O (lambda(n-1...
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作者：Ford, Kevin; Ben Green; Koukoulopoulos, Dimitris
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Oxford; Universite de Montreal
摘要：We study the extent to which divisors of a typical integer n are concentrated. In particular, defining Delta(n) := max(t) #{d vertical bar n, log d is an element of [t, t + 1]}, we show that Delta(n) >= (log log n)(0.35332277...) for almost all n, a bound we believe to be sharp. This disproves a conjecture of Maier and Tenenbaum. We also prove analogs for the concentration of divisors of a random permutation and of a random polynomial over a finite field. Most of the paper is devoted to a stud...
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作者：Fujiwara, Koji; Sela, Zlil
作者单位：Kyoto University; Hebrew University of Jerusalem
摘要：We study the countable set of rates of growth of a hyperbolic group with respect to all its finite generating sets. We prove that the set is well-ordered, and that every real number can be the rate of growth of at most finitely many generating sets up to automorphism of the group. We prove that the ordinal of the set of rates of growth is at least omega(omega 0)(0), and in case the group is a limit group (e.g. free and surface groups) it is omega(omega 0)(0). We further study the rates of grow...
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作者：Roendigs, Oliver
作者单位：University Osnabruck
摘要：The endomorphism ring of the projective plane over a field F of characteristic neither two nor three is slightly more complicated in the Morel-Voevodsky motivic stable homotopy category than in Voevodsky's derived category of motives. In particular, it is not commutative precisely if there exists a square in F which does not admit a sixth root. A byproduct of these computations is a proof of Suslin's conjecture on the Suslin-Hurewicz homomorphism from Quillen to Milnor K-theory in degree four,...
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作者：Nelson, Paul D.
作者单位：Aarhus University
摘要：Let (pi, sigma) traverse a sequence of pairs of cuspidal automorphic representations of a unitary Gan-Gross-Prasad pair (Un+1, U-n) over a number field, with Un anisotropic. We assume that at some distinguished archimedean place, the pair stays away from the conductor dropping locus, while at every other place, the pair has bounded ramification and satisfies certain local con-ditions (in particular, temperedness). We prove that the subconvex bound L(pi x sigma, 1/2) << C(pi x sigma )(1/4-delta...
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作者：Alper, Jarod; Halpern-Leistner, Daniel; Heinloth, Jochen
作者单位：University of Washington; University of Washington Seattle; Cornell University; University of Duisburg Essen
摘要：We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for points of algebraic stacks equipped with a T-stratification. These results provide a generalization of the Keel-Mori theorem to moduli problems whose objects have positive dimensional automorphism groups and give criteria on the moduli problem to have a separated or proper good moduli space. To illustrate our method, we apply these results to constr...
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作者：Ivanov, Sergei; Mamaev, Daniil; Nordskova, Anya
作者单位：Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; Hasselt University
摘要：We prove that if all intersections of a convex body B subset of R-4 with 3-dimensional linear subspaces are linearly equivalent then B is a centered ellipsoid. This gives an affirmative answer to the case n = 3 of the following question by Banach from 1932: Is a normed vector space V whose n-dimensional linear subspaces are all isometric, for a fixed 2 <= n < dim V, necessarily Euclidean? The dimensions n = 3 and dim V = 4 is the first case where the question was unresolved. Since the 3-sphere...
