Journal of the London Mathematical Society-Second Series最新文献

We prove two estimates for the Barban–Davenport–Halberstam type variance of a general complex sequence in arithmetic progressions. The proofs are elementary, and our estimates are capable of yielding an asymptotic for the variance when the sequence is sufficiently nice, and is either somewhat sparse or is sufficiently like the integers in its divisibility by small moduli. As a concrete application, we deduce a Barban–Davenport–Halberstam type variance asymptotic for the $�y$-smooth numbers less than $�x$, on a wide range of the parameters. This addresses a question considered by Granville and Vaughan. Our methods also recover some earlier results for the case of prime numbers.

We study several natural decision problems in braid groups and Artin groups. We classify the Artin groups with decidable submonoid membership problem in terms of the nonexistence of certain forbidden-induced subgraphs of the defining graph. Furthermore, we also classify the Artin groups for which the following problems are decidable: the rational subset membership problem, semigroup intersection problem, and the fixed-target submonoid membership problem. In the case of braid groups, our results show that the submonoid membership problem, and each and every one of these problems, is decidable in the braid group $�B_n$ if and only if $��n�⩽�3�$, which answers an open problem of Potapov (2013). Our results also generalize and extend results of Lohrey and Steinberg (2008) who classified right-angled Artin groups with decidable submonoid (and rational subset) membership problem.

We derive a parabolic–elliptic coupled system as a new simplified model for the hydrodynamics of radiating gas with viscosity and thermal conductivity. This model captures the interplay between viscous dissipation and nonlocal radiative effect. Our main contributions are the establishment of unconditional global stability of solutions to the Cauchy problem for constant states, rarefaction waves, and planar rarefaction waves under different initial conditions, and the derivation of precise decay rates for the asymptotic behaviors of solutions. Unlike previous studies, our results do not require any smallness assumptions on the initial perturbation or wave strength. This can be viewed as the first result on the unconditional global stability for fluid dynamics equations. Our analysis relies on a combination of energy estimates, maximum principle and Fourier analysis, with the dissipation term playing a crucial role in controlling nonlinear effect.

We study gradient regularity for mixed local–nonlocal problems modeled upon

A special type of geometric situation in ensembles of nonintersecting paths occurs when the nonintersecting trajectories are required to be nonnegative so that the limit shape becomes tangential to the hard-edge 0. The local fluctuation is governed by the universal hard edge tacnode process, which also arises from some tiling problems. It is the aim of this work to explore the integrable structure and asymptotics for the gap probability of the hard edge thinned/unthinned tacnode process over $��(�0�,�s�)�$. We establish an integral representation of the gap probability in terms of the Hamiltonian associated with a system of differential equations. With the aids of some remarkable differential identities for the Hamiltonian, we are able to derive the associated large gap asymptotics, up to and including the constant term in the thinned case. Some applications of our results are discussed as well.

The aim of this paper is to characterize universal and multiplier interpolating sequences for de Branges–Rovnyak spaces $��H�\left(�b�\right)�$ where the defining function $�b$ is a general non-extreme rational function. Our results carry over to recently introduced higher order local Dirichlet spaces and thus generalize previously known results in classical local Dirichlet spaces. In this setting, we also investigate random interpolating sequences with prescribed radii, providing a 0-1 law.

We consider the joint value distribution of Dirichlet $�L$-functions in the critical strip . We show that the values of distinct Dirichlet $�L$-functions are dependent in the sense that they do not behave like independently distributed random variables and they prevent each other from obtaining large values. Nevertheless, we show that distinct Dirichlet $�L$-functions can achieve large values simultaneously infinitely often.