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Overconvergent quaternionic forms and anticyclotomic p-adic L-functions
https://ddd.uab.cat/record/206886
We reinterpret the explicit construction of Gross points given by Chida-Hsieh as a non-Archimedian analogue of the standard geodesic cycle (i∞)-(0) on the Poincaré upper half plane. This analogy allows us to consider certain distributions, which can be regarded as anticyclotomic p-adic L-functions for modular forms of non-critical slope following the overconvergent strategy à la Stevens. We also give a geometric interpretation of their Gross points for the case of weight two forms. Our construction generalizes those of Bertolini-Darmon, Bertolini-Darmon-Iovita-Spiess,-and Chida-Hsieh and shows a certain integrality of the interpolation formula even for non-ordinary forms. Kim, Chan-HoTue, 02 Jul 2019 04:44:32 GMThttps://ddd.uab.cat/record/2068862019An interpolation property of locally Stein sets
https://ddd.uab.cat/record/206885
We prove that, if D is a normal open subset of a Stein space X of puredimension such that D is locally Stein at every point of ∂D n Xsg, then, for every holomorphic vector bundle E over D and every discrete subset Ʌ of D \ Xsg whose set of accumulation points lies in ∂D \ Xsg, there is a holomorphic section of E over D with prescribed values on Ʌ. We apply this to the local Steinness problem and domains of holomorphy. Vâjâitu, ViorelTue, 02 Jul 2019 04:44:32 GMThttps://ddd.uab.cat/record/2068852019The boundedness of multilinear Calderón-Zygmund operators on weighted and variable Hardy spaces
https://ddd.uab.cat/record/206884
We establish the boundedness of the multilinear Calderon{Zygmund operators from a product of weighted Hardy spaces into a weighted Hardy or Lebesgue space. Our results generalize to the weighted setting results obtained by Grafakos and Kalton [18] and recent work by the third author, Grafakos, Nakamura, and Sawano [20]. As part of our proof we provide a finite atomic decomposition theorem for weighted Hardy spaces, which is interesting in its own right. As a consequence of our weighted results, we prove the corresponding estimates on variable Hardy spaces. Our main tool is a multilinear extrapolation theorem that generalizes a result of the first author and Naibo [10]. Cruz-Uribe, DavidTue, 02 Jul 2019 04:44:32 GMThttps://ddd.uab.cat/record/2068842019Characterization of Sobolev-Slobodeckij spaces using geometric curvature energies
https://ddd.uab.cat/record/206883
We give a new characterization of Sobolev–Slobodeckij spaces W1+s,pfor n/p < 1+s, where n is the dimension of the domain. To achieve this we introduce a family of curvature energies inspired by the classical concept of integral Menger curvature. We prove that a function belongs to a Sobolev–Slobodeckij space if and only if it is in Lp and the appropriate energy is finite. Dabrowski, DamianTue, 02 Jul 2019 04:44:32 GMThttps://ddd.uab.cat/record/2068832019Bandlimited approximations and estimates for the Riemann zeta-function
https://ddd.uab.cat/record/206882
In this paper we provide explicit upper and lower bounds for the argument of the Riemann zeta-function and its antiderivatives in the critical strip under the assumption of the Riemann hypothesis. This extends the previously known bounds for these quantities on the critical line (and sharpens the error terms in such estimates). Our tools come not only from number theory, but also from Fourier analysis and approximation theory. An important element in our strategy is the ability to solve a Fourier optimization problem with constraints, namely, the problem of majorizing certain real-valued even functions by bandlimited functions, optimizing the L1(R)-error. Deriving explicit formulae for the Fourier transforms of such optimal approximations plays a crucial role in our approach. Carneiro, EmanuelTue, 02 Jul 2019 04:44:32 GMThttps://ddd.uab.cat/record/2068822019Pavage de Voronoï associé au groupe de Cremona
https://ddd.uab.cat/record/206881
The action of the Cremona group of rank 2 on an infinite dimensionalhyperbolic space is the main recent tool to study the Cremona group. Following the analogy with the action of PSL(2; Z) on the Poincare half-plane, we exhibit a fundamental domain for this action by considering a Voronoi tessellation. Then we study adjacent cells to a given cell, as well as cells that share common points in the boundary at infinity. Lonjou, AnneTue, 02 Jul 2019 04:44:32 GMThttps://ddd.uab.cat/record/2068812019Rectifiability of measures and the βp coefficients
https://ddd.uab.cat/record/206880
In some former works of Azzam and Tolsa it was shown that n-rectifiabilitycan be characterized in terms of a square function involving the David-Semmes β2 coecients. In the present paper we construct some counterexamples which show that a similar characterization does not hold for the βp coefficients with p = 2. This is in strong contrast with what happens in the case of uniform n-rectifiability. In the second part of this paper we provide an alternative argument for a recent result of Edelen, Naber, and Valtorta about the n-rectifiability of measures with bounded lower n-dimensional density. Our alternative proof follows from a slight variant of the corona decomposition in one of the aforementioned works of Azzam and Tolsa and a suitable approximation argument. Tolsa Domènech, XavierTue, 02 Jul 2019 04:44:32 GMThttps://ddd.uab.cat/record/2068802019Some new examples of simple p-local compact groups
https://ddd.uab.cat/record/206879
In this paper we present new examples of simple p-local compact groupsfor all odd primes. We also develop the necessary tools to show saturation, simpleness, and the non-realizability as p-compact groups or compact Lie groups, which can be applied in a more general framework. González, ÁlexTue, 02 Jul 2019 04:44:32 GMThttps://ddd.uab.cat/record/2068792019Five solved problems on radicals of ore extensions
https://ddd.uab.cat/record/206878
We answer several open questions and establish new results concerningdierential and skew polynomial ring extensions, with emphasis on radicals. In particular, we prove the following results. If R is prime radical and δ is a derivation of R, then the dierential polynomial ring R[X; δ] is locally nilpotent. This answers an open question posed in [41]. The nil radical of a dierential polynomial ring R[X; δ] takes the form I[X; δ] for some ideal I of R, provided that the base field is infinite. This answers an open question posed in [30] for algebras over infinite fields. If R is a graded algebra generated in degree 1 over a field of characteristic zero and δ is a grading preserving derivation on R, then the Jacobson radical of R is δ-stable. Examples are given to show the necessity of all conditions, thereby proving this result is sharp. Skew polynomial rings with natural grading are locally nilpotent if and only if they are graded locally nilpotent. The power series ring R[[X; σ; δ]] is well-defined whenever δ is a locally nilpotent σ-derivation; this answers a conjecture from [13], and opens up the possibility of generalizing many research directions studied thus far only when further restrictions are put on δ. Greenfeld, Be'eriTue, 02 Jul 2019 04:44:32 GMThttps://ddd.uab.cat/record/2068782019The linear nature of pseudowords
https://ddd.uab.cat/record/206877
Given a pseudoword over suitable pseudovarieties, we associate to it alabeled linear order determined by the factorizations of the pseudoword. We show that, in the case of the pseudovariety of aperiodic finite semigroups, the pseudoword can be recovered from the labeled linear order. Almeida, JorgeTue, 02 Jul 2019 04:44:32 GMThttps://ddd.uab.cat/record/2068772019Lattice points in elliptic paraboloids
https://ddd.uab.cat/record/200755
We consider the lattice point problem corresponding to a family of elliptic paraboloids in Rd with d ≥ 3 and we prove the expected to be optimal exponent, improving previous results. This is especially noticeable for d = 3 because the optimal exponent is conjectural even for the sphere. We also treat some aspects of the case d = 2, getting for a simple parabolic region an Ω-result that is unknown for the classical circle and divisor problems. Chamizo Lorente, FernandoTue, 08 Jan 2019 06:42:06 GMThttps://ddd.uab.cat/record/2007552019Distinguishing Hermitian cusp forms of degree 2 by a certain subset of all Fourier coefficients
https://ddd.uab.cat/record/200754
We prove that Hermitian cusp forms of weight k for the Hermitian modular group of degree 2 are determined by their Fourier coefficients indexed by matrices whose determinants are essentially square-free. Moreover, we give a quantitative version of the above result. This is a consequence of the corresponding results for integral weight elliptic cusp forms, which are also treated in this paper. Anamby, PramathTue, 08 Jan 2019 06:42:06 GMThttps://ddd.uab.cat/record/2007542019Holonomy representation of quasi-projective leaves of codimension one foliations
https://ddd.uab.cat/record/200753
We prove that a representation of the fundamental group of a quasiprojective manifold into the group of formal diffeomorphisms of one variable either is virtually abelian or, after taking the quotient by its center, factors through an orbicurve. Claudon, BenoîtTue, 08 Jan 2019 06:42:06 GMThttps://ddd.uab.cat/record/2007532019Simplicial Lusternik–Schnirelmann category
https://ddd.uab.cat/record/200752
The simplicial LS-category of a finite abstract simplicial complex is a new invariant of the strong homotopy type, defined in purely combinatorial terms. We prove that it generalizes to arbitrary simplicial complexes the well known notion of arboricity of a graph, and that it allows to develop many notions and results of algebraic topology which are costumary in the classical theory of Lusternik–Schnirelmann category. Also we compare the simplicial category of a complex with the LS-category of its geometric realization and we discuss the simplicial analogue of the Whitehead formulation of the LS-category. Fernandez-Ternero, DesamparadosTue, 08 Jan 2019 06:42:06 GMThttps://ddd.uab.cat/record/2007522019Weak-2-local isometries on uniform algebras and Lipschitz algebras
https://ddd.uab.cat/record/200751
We establish spherical variants of the Gleason–Kahane–Zelazko and Kowalski–S lodkowski theorems, and we apply them to prove that every weak-2-local isometry between two uniform algebras is a linear map. Among the consequences, we solve a couple of problems posed by O. Hatori, T. Miura, H. Oka, and H. Takagi in 2007. Another application is given in the setting of weak-2-local isometries between Lipschitz algebras by showing that given two metric spaces E and F such that the set Iso((Lip(E), k·k), (Lip(F), k·k)) is canonical, then every weak-2-local Iso((Lip(E), k · k), (Lip(F), k · k))-map ∆ from Lip(E) to Lip(F) is a linear map, where k · k can indistinctly stand for kfkL := max{L(f), kfk∞} or kfks := L(f) + kfk∞. Li, LeiTue, 08 Jan 2019 06:42:06 GMThttps://ddd.uab.cat/record/2007512019Growth alternative for Hecke–Kiselman monoids
https://ddd.uab.cat/record/200750
The Gelfand–Kirillov dimension of Hecke–Kiselman algebras defined by oriented graphs is studied. It is shown that the dimension is infinite if and only if the underlying graph contains two cycles connected by an (oriented) path. Moreover, in this case, the Hecke–Kiselman monoid contains a free noncommutative submonoid. The dimension is finite if and only if the monoid algebra satisfies a polynomial identity. Meçel, ArkadiuszTue, 08 Jan 2019 06:42:06 GMThttps://ddd.uab.cat/record/2007502019Primitive geodesic lengths and (almost) arithmetic progressions
https://ddd.uab.cat/record/200749
In this article we investigate when the set of primitive geodesic lengths on a Riemannian manifold have arbitrarily long arithmetic progressions. We prove that in the space of negatively curved metrics, a metric having such arithmetic progressions is quite rare. We introduce almost arithmetic progressions, a coarsification of arithmetic progressions, and prove that every negatively curved, closed Riemannian manifold has arbitrarily long almost arithmetic progressions in its primitive length spectrum. Concerning genuine arithmetic progressions, we prove that every noncompact, locally symmetric, arithmetic manifold has arbitrarily long arithmetic progressions in its primitive length spectrum. We end with a conjectural characterization of arithmeticity in terms of arithmetic progressions in the primitive length spectrum. We also suggest an approach to a well known spectral rigidity problem based on the scarcity of manifolds with arithmetic progressions. Lafont, Jean FrançoisTue, 08 Jan 2019 06:42:05 GMThttps://ddd.uab.cat/record/2007492019Rescaled extrapolation for vector-valued functions
https://ddd.uab.cat/record/200748
We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results. In particular we prove Littlewood–Paley–Rubio de Francia-type estimates and boundedness of variational Carleson operators for Banach function spaces with UMD concavifications. Amenta, AlexTue, 08 Jan 2019 06:42:05 GMThttps://ddd.uab.cat/record/2007482019Sullivan minimal models of operad algebras
https://ddd.uab.cat/record/200747
We prove the existence of Sullivan minimal models of operad algebras for a quite wide family of operads in the category of complexes of vector spacesover a field of characteristic zero. Our construction is an adaptation of Sullivan's original step by step construction to the setting of operad algebras. The family of operads that we consider includes all operads concentrated in degree 0 as well as their minimal models. In particular, this gives Sullivan minimal models for algebras over Com, Ass, and Lie, as well as over their minimal models Com∞, Ass∞, and Lie∞. Other interesting operads, such as the operad Ger encoding Gerstenhaber algebras, also fit in our study. Cirici, JoanaTue, 08 Jan 2019 06:42:05 GMThttps://ddd.uab.cat/record/2007472019Topological classification of limit periodic sets of polynomial planar vector fields
https://ddd.uab.cat/record/200746
We characterize the limit periodic sets of families of algebraic planar vector fields up to homeomorphisms. We show that any limit periodic set is topologically equivalent to a compact and connected semialgebraic set of the sphere of dimension 0 or 1. Conversely, we show that any compact and connected semialgebraic set of the sphere of dimension 0 or 1 can be realized as a limit periodic set. da Silva, Andre BelottoTue, 08 Jan 2019 06:42:05 GMThttps://ddd.uab.cat/record/2007462019Moduli spaces of a family of topologically non quasi-homogeneous functions
https://ddd.uab.cat/record/200745
We consider a topological class of a germ of complex analytic function in two variables which does not belong to its jacobian ideal. Such a function is not quasi homogeneous. Each element f in this class induces a germ of foliation (df = 0). Proceeding similarly to the homogeneous case [2] and the quasi homogeneous case [3] treated by Genzmer and Paul, we describe the local moduli space of the foliations in this class and give analytic normal forms. We prove also the uniqueness of these normal forms. Loubani, JinanTue, 08 Jan 2019 06:42:05 GMThttps://ddd.uab.cat/record/2007452019Asymptotic expansions and summability with respect to an analytic germ
https://ddd.uab.cat/record/200744
In a previous article [CMS], monomial asymptotic expansions, Gevrey asymptotic expansions, and monomial summability were introduced and applied to certain systems of singularly perturbed differential equations. In the present work, we extend this concept, introducing (Gevrey) asymptotic expansions and summability with respect to a germ of an analytic function in several variables – this includes polynomials. The reduction theory of singularities of curves and monomialization of germs of analytic functions are crucial to establish properties of the new notions, for example a generalization of the Ramis–Sibuya theorem for the existence of Gevrey asymptotic expansions. Two examples of singular differential equations are presented for which the formal solutions are shown to be summable with respect to a polynomial: one ordinary and one partial differential equation. Mozo Fernandez, JorgeTue, 08 Jan 2019 06:42:05 GMThttps://ddd.uab.cat/record/2007442019Lifting non-ordinary cohomology classes for SL3
https://ddd.uab.cat/record/191244
In this paper, we present a generalisation of a theorem of David and Rob Pollack. In [PP], they give a very general argument for lifting ordinary eigenclasses(with respect to a suitable operator) in the group cohomology of certain arithmetic groups. With slightly tighter conditions, we prove the same result for non-ordinary classes. Pollack and Pollack apply their results to the case of p-ordinary classes in the group cohomology of congruence subgroups for SL3, constructing explicit overconvergent classes in this setting. As an application of our results, we give an extension of their results to the case of non-critical slope classes in the same setting. Williams, ChrisTue, 26 Jun 2018 03:06:16 GMThttps://ddd.uab.cat/record/1912442018A characterization of finite multipermutation solutions of the Yang-Baxter equation
https://ddd.uab.cat/record/191243
We prove that a finite non-degenerate involutive set-theoretic solution (X, r) of the Yang-Baxter equation is a multipermutation solution if and only if its structure group G(X, r) admits a left ordering or equivalently it is poly-Z. Bachiller Pérez, DavidTue, 26 Jun 2018 03:06:16 GMThttps://ddd.uab.cat/record/1912432018Determinants of Laplacians on Hilbert modular surfaces
https://ddd.uab.cat/record/191242
We study regularized determinants of Laplacians acting on the space of Hilbert-Maass forms for the Hilbert modular group of a real quadratic field. Weshow that these determinants are described by Selberg type zeta functions introduced in [5, 6]. Gon, YasuroTue, 26 Jun 2018 03:06:16 GMThttps://ddd.uab.cat/record/1912422018