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  • COMBINATORIAL INSCRIBABILITY OBSTRUCTIONS FOR HIGHER DIMENSIONAL POLYTOPES
    Mathematika (IF 0.875) Pub Date : 2020-08-07
    Joseph Doolittle; Jean‐Philippe Labbé; Carsten E. M. C. Lange; Rainer Sinn; Jonathan Spreer; Günter M. Ziegler

    For 3‐dimensional convex polytopes, inscribability is a classical property that is relatively well‐understood due to its relation with Delaunay subdivisions of the plane and hyperbolic geometry. In particular, inscribability can be tested in polynomial time, and for every f‐vector of 3‐polytopes, there exists an inscribable polytope with that f‐vector. For higher dimensional polytopes, much less is

    更新日期:2020-08-08
  • CONCRETE POLYTOPES MAY NOT TILE THE SPACE
    Mathematika (IF 0.875) Pub Date : 2020-07-16
    Alexey Garber; Igor Pak

    Brandolini et al . conjectured in (Preprint , 2019) that all concrete lattice polytopes can multitile the space. We disprove this conjecture in a strong form, by constructing an infinite family of counterexamples in R 3 .

    更新日期:2020-07-16
  • SPECTRA OF DELAY EQUATIONS
    Mathematika (IF 0.875) Pub Date : 2020-07-08
    Luis Barreira; Claudia Valls

    We describe all possible forms of the Sacker–Sell spectrum for a nonautonomous linear delay equation. In particular, the spectrum may have infinitely many connected components either accumulating at minus infinity or at a finite value. We also show that to each connected component of the spectrum one can associate a subspace of initial conditions whose lower and upper Lyapunov exponents are contained

    更新日期:2020-07-08
  • AUTOMORPHIC SL2‐PERIODS AND THE SUBCONVEXITY PROBLEM FOR GL2 × GL3
    Mathematika (IF 0.875) Pub Date : 2020-07-03
    Aprameyo Pal; Carlos de Vera‐Piquero

    We prove a new (conditional) result toward the subconvexity problem for certain automorphic L‐functions for GL2 × GL3. This follows from the computation of new SL2‐period integrals associated with newforms f and g of even weight and odd squarefree level. The same computations also lead to a central value formula for degree six complex L‐series of the form L ( f ⊗ Ad ( g ) , s ) , extending previous

    更新日期:2020-07-03
  • AN OPTIMAL BOUND FOR THE RATIO BETWEEN ORDINARY AND UNIFORM EXPONENTS OF DIOPHANTINE APPROXIMATION
    Mathematika (IF 0.875) Pub Date : 2020-06-28
    Antoine Marnat; Nikolay G. Moshchevitin

    We provide a lower bound for the ratio between the ordinary and uniform exponents of both simultaneous Diophantine approximation to n real numbers and Diophantine approximation for one linear form in n variables. This question was first considered in the 1950s by Jarník who solved the problem for two real numbers and established certain bounds in higher dimension. Recently different authors reconsidered

    更新日期:2020-06-29
  • SATURATION FOR THE BUTTERFLY POSET
    Mathematika (IF 0.875) Pub Date : 2020-05-20
    Maria‐Romina Ivan

    Given a finite poset P , we call a family F of subsets of [n ] P ‐saturated if F does not contain an induced copy of P , but adding any other set to F creates an induced copy of P . The induced saturated number of P , denoted by sat ∗ ( n , P ) , is the size of the smallest P ‐saturated family with ground set [n ]. In this paper, we are mainly interested in the four‐point poset called the butterfly

    更新日期:2020-05-20
  • LOW‐LYING ZEROS OF L‐FUNCTIONS FOR MAASS FORMS OVER IMAGINARY QUADRATIC FIELDS
    Mathematika (IF 0.875) Pub Date : 2020-05-13
    Sheng‐Chi Liu; Zhi Qi

    We study the 1‐ or 2‐level density of families of L‐functions for Hecke–Maass forms over an imaginary quadratic field F. For test functions whose Fourier transform is supported in ( − 3 2 , 3 2 ) , we prove that the 1‐level density for Hecke–Maass forms over F of square‐free level q , as N ( q ) tends to infinity, agrees with that of the orthogonal random matrix ensembles. For Hecke–Maass forms over

    更新日期:2020-05-13
  • ITERATIONS OF CURVATURE IMAGES
    Mathematika (IF 0.875) Pub Date : 2020-05-10
    Mohammad N. Ivaki

    We study the iterations of a class of curvature image operators Λ p φ introduced by Ivaki in [J. Funct. Anal. 271 (2016) 2133–2165]. The fixed points of these operators are the solutions of the L p Minkowski problems with the positive continuous prescribed data φ. One of our results states that if p ∈ ( − n , 1 ) and φ is even, or if p ∈ ( − n , − n + 1 ] , then the iterations of these operators applied

    更新日期:2020-05-10
  • EIGENVALUES OF THE FINSLER p‐LAPLACIAN ON VARYING DOMAINS
    Mathematika (IF 0.875) Pub Date : 2020-05-07
    Giuseppina di Blasio; Pier Domenico Lamberti

    We study the dependence of the first eigenvalue of the Finsler p‐Laplacian and the corresponding eigenfunctions on perturbation of the domain and we generalize a few results known for the standard p‐Laplacian. In particular, we prove a Frechét differentiability result for the eigenvalues, compute the corresponding Hadamard formulas and prove a continuity result for the eigenfunctions. Finally, we briefly

    更新日期:2020-05-07
  • NORMAL TILINGS OF A BANACH SPACE AND ITS BALL
    Mathematika (IF 0.875) Pub Date : 2020-05-06
    Robert Deville; Miguel García‐Bravo

    We show some new results about tilings in Banach spaces. A tiling of a Banach space X is a covering by closed sets with non‐empty interior, so that they have pairwise disjoint interiors. If, moreover, the tiles have inner radii uniformly bounded from below, and outer radii uniformly bounded from above, we say that the tiling is normal. In 2010, Preiss constructed a convex normal tiling of the separable

    更新日期:2020-05-06
  • HOMOGENEOUS COMPLETELY SIMPLE SEMIGROUPS
    Mathematika (IF 0.875) Pub Date : 2020-05-05
    Thomas Quinn‐Gregson

    A semigroup is completely simple if it has no proper ideals and contains a primitive idempotent. We say that a completely simple semigroup S is a homogeneous completely simple semigroup if any isomorphism between finitely generated completely simple sub‐semigroups of S extends to an automorphism of S. Motivated by the study of homogeneous completely regular semigroups, we obtain a complete classification

    更新日期:2020-05-05
  • BEYOND ARTIN'S CONJECTURE FOR CUBIC FORMS
    Mathematika (IF 0.875) Pub Date : 2020-05-04
    Miriam Sophie Kaesberg

    It is established that every cubic form in at least eight variables which can be realised as a diagonal form on a hyperplane has a non‐trivial p‐adic solution for all primes p.

    更新日期:2020-05-04
  • EXPONENTIAL MOMENTS OF THE ARGUMENT OF THE RIEMANN ZETA FUNCTION ON THE CRITICAL LINE
    Mathematika (IF 0.875) Pub Date : 2020-05-04
    Joseph Najnudel

    In this article, we give, under the Riemann hypothesis, an upper bound for the exponential moments of the imaginary part of the logarithm of the Riemann zeta function on the critical line. Our result, which gives information on the fluctuations of the distribution of the zeros of ζ, has the same accuracy as the result obtained by Soundararajan (Ann. of Math. (2) 170(2) (2009), 981–993) for the moments

    更新日期:2020-05-04
  • VARIATIONAL INEQUALITIES FOR BILINEAR AVERAGES
    Mathematika (IF 0.875) Pub Date : 2020-05-04
    Honghai Liu; Hanbin Wang

    We establish variational inequalities for a class of bilinear averages of one variable, generalizing the variational inequalities for linear averages of Jones et al. As an application we obtain almost everywhere convergence for ergodic averages along cubes on a dynamical system.

    更新日期:2020-05-04
  • NOWHERE‐ANALYTIC SMOOTH CURVES WITH NON‐TRIVIAL ANALYTIC ISOTROPY
    Mathematika (IF 0.875) Pub Date : 2020-05-04
    Giuseppe Della Sala

    We study the smoothness properties of planar curves γ ⊂ R 2 , 0 ∈ γ , which are invariant under a local real‐analytic diffeomorphism ψ fixing the origin. Under certain conditions, depending on the first‐order jet (if the eigenvalues of d ψ ( 0 ) are not both of modulus one) or on a higher order jet (if ψ is tangent to the identity) of ψ and γ, we show that γ must be real analytic as soon as it is smooth

    更新日期:2020-05-04
  • EFFECTIVE l2 DECOUPLING FOR THE PARABOLA
    Mathematika (IF 0.875) Pub Date : 2020-05-04
    Zane Kun Li

    We make effective l 2 L p decoupling for the parabola in the range 4 < p < 6 . In an appendix joint with Jean Bourgain, we apply the main theorem to prove the conjectural bound for the sixth‐order correlation of the integer solutions of the equation x 2 + y 2 = m in an extremal case. This proves unconditionally a result that was proven in Bombieri and Bourgain [Int. Math. Res. Not. IMRN 2015(11), 3343–3407]

    更新日期:2020-05-04
  • POISSON HYPERPLANE PROCESSES AND APPROXIMATION OF CONVEX BODIES
    Mathematika (IF 0.875) Pub Date : 2020-05-04
    Daniel Hug; Rolf Schneider

    A natural model for the approximation of a convex body K in R d by random polytopes is obtained as follows. Take a stationary Poisson hyperplane process in R d , and consider the random polytope Z K defined as the intersection of all closed halfspaces containing K that are bounded by hyperplanes of the process not intersecting K. If f is a functional on convex bodies, then for increasing intensities

    更新日期:2020-05-04
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