Mathematische Zeitschrift最新文献

We present a new random approximation method that yields the existence of a discrete Beurling prime system (mathcal {P}={p_{1}, p_{2}, cdots }) which is very close in a certain precise sense to a given non-decreasing, right-continuous, nonnegative, and unbounded function F. This discretization procedure improves an earlier discrete random approximation method due to Diamond et al. (Math Ann 334:1–36, 2006), and refined by Zhang (Math Ann 337:671–704, 2007). We obtain several applications. Our new method is applied to a question posed by Balazard concerning Dirichlet series with a unique zero in their half plane of convergence, to construct examples of very well-behaved generalized number systems that solve a recent open question raised by Hilberdink and Neamah (Int J Number Theory 16(05):1005–1011, 2020), and to improve the main result from (Adv Math 370:Article 107240, 2020), where a Beurling prime system with regular primes but extremely irregular integers was constructed.

In this paper we prove two unboundedness results about the Tate–Shafarevich groups of abelian varieties in a fixed nontrivial cyclic extension L/K of global fields, firstly in the case that K is a number field and the abelian varieties are elliptic curves, secondly in the case that K is a global field, [L : K] is a 2-power and the abelian varieties are principally polarized.

We introduce the notion of fibered lifted partially hyperbolic diffeomorphisms and we prove that any partially hyperbolic diffeomorphism isotopic to a fibered lifted one where the isotopy take place inside partially hyperbolic systems is dynamically coherent. Moreover we prove some global stability result: every two partially hyperbolic diffeomorphisms in the same connected component of a fibered lifted partially hyperbolic diffeomorphisms are leaf conjugate.

In this paper, we prove the long neck principle, band width estimates, and width inequalities of the geodesic collar neighborhoods of the boundary in the setting of general initial data sets for the Einstein equations, subject to certain energy conditions corresponding to the lower bounds of scalar curvature on Riemannian manifolds. Our results are established via the spinorial Callias operator approach.

In this paper, the structure of the nearly invariant subspaces for discrete semigroups generated by several (even infinitely many) automorphisms of the unit disc is described. As part of this work, the near (S^*)-invariance property of the image space (C_varphi (ker T)) is explored for composition operators (C_varphi ), induced by inner functions (varphi ), and Toeplitz operators T. After that, the analysis of nearly invariant subspaces for strongly continuous multiplication semigroups of isometries is developed with a study of cyclic subspaces generated by a single Hardy class function. These are characterised in terms of model spaces in all cases when the outer factor is a product of an invertible function and a rational (not necessarily invertible) function. Techniques used include the theory of Toeplitz kernels and reproducing kernels.

We study immersions of Sasakian manifolds into finite and infinite dimensional Sasakian space forms. After proving Calabi’s rigidity results in the Sasakian setting, we characterise all homogeneous Sasakian manifolds which admit a (local) Sasakian immersion into a nonelliptic Sasakian space form. Moreover, we give a characterisation of homogeneous Sasakian manifolds which can be embedded into the standard sphere both in the compact and noncompact case.

Given a nonnegative integrable function J on (mathbb {R}^n), we relate the asymptotic properties of the nonlocal energy functional

as (t rightarrow 0^+) with the boundary properties of a given domain (Omega subset mathbb {R}^n), focusing mainly on domains with “rough” boundaries. Then, we apply these results to the fluctuations of many determinantal point processes, showing (under suitable hypotheses) that their variances measure the Minkowski dimension of (partial Omega ).

This paper provides a characterization of when two expansive matrices yield the same anisotropic local Hardy and inhomogeneous Triebel–Lizorkin spaces. The characterization is in terms of the coarse equivalence of certain quasi-norms associated to the matrices. For nondiagonal matrices, these conditions are strictly weaker than those classifying the coincidence of the corresponding homogeneous function spaces. The obtained results complete the classification of anisotropic Besov and Triebel–Lizorkin spaces associated to general expansive matrices.

We consider a perturbation of the Benjamin Ono equation with periodic boundary conditions on a segment. We consider the case where the perturbation is Hamiltonian and the corresponding Hamiltonian vector field is analytic as a map from the energy space to itself. Let (epsilon ) be the size of the perturbation. We prove that for initial data close in energy norm to an N-gap state of the unperturbed equation all the actions of the Benjamin Ono equation remain ({mathcal {O}}(epsilon ^{frac{1}{2(N+1)}})) close to their initial value for times exponentially long with (epsilon ^{-frac{1}{2(N+1)}}).

We show that the morphism (Omega ) from the (imath )quantum loop algebra ({}^{text {Dr}}widetilde{{{textbf{U}}}}^imath (L{mathfrak {g}})) of split type to the (imath )Hall algebra of the weighted projective line is injective if ({mathfrak {g}}) is of finite or affine type. As a byproduct, we use the whole (imath )Hall algebra of the cyclic quiver (C_n) to realize the (imath )quantum loop algebra of affine (mathfrak {gl}_n).