相关论文: Addendum to "On the $p^{\lambda}$ problem"

In this paper, I present a natural generalization of all the results from [6] to LVMB manifolds: to summarize, very few LVMB manifolds are lck, and none are lck with potential except for diagonal Hopf manifolds. Moreover, if $N$ is an LVMB…

In this paper, we study Thrall's problem for the higher Lie modules $L_\lambda$. Our main result provides a tableau-theoretic description of the Schur expansion of the character of $L_\lambda$ when $\lambda$ has two rows, thereby solving…

We obtain a necessary and sufficient condition for embeddings of integral Lipschitz classes Lip(\alpha; p) into classes \Lambda BV of functions of bounded \Lambda-variation.

This paper studies explicit and theoretical bounds for several interesting quantities in number theory, conditionally on the Generalized Riemann Hypothesis. Specifically, we improve the existing explicit bounds for the least quadratic…

We prove for any mu = mu^{< mu}< theta < lambda, lambda large enough (just strongly inaccessible Mahlo) the consistency of 2^mu = lambda-> [theta]^2_3 and even 2^mu = lambda-> [theta]^2_{sigma,2} for sigma < mu . The new point is that…

We prove that the almost sure Lyapunov exponent \lambda(\kappa) of the continuous space Parabolic Anderson Model is bounded above by $c_u \kappa^{1/3}$ as $\kappa\downarrow0$ under mild regularity conditions. This bound of the same order of…

We adapt an argument of Tao and Vu to show that if $\lambda_1\le\cdots\le\lambda_d$ are the successive minima of an origin-symmetric convex body $K$ with respect to some lattice $\Lambda<\mathbb{R}^d$, and if we set…

In this note we give a short and self-contained proof that, for any $\delta > 0$, $\sum_{x \leq n \leq x+x^\delta} \lambda(n) = o(x^\delta)$ for almost all $x \in [X, 2X]$. We also sketch a proof of a generalization of such a result to…

We generalize two embedding theorems and investigate the existence and multiplicity of nontrivial solutions for a $(p,q)$-Laplacian coupled system with perturbations and two parameters $\lambda_1$ and $\lambda_2$ on locally finite graph. By…

For a partition {\lambda} and a prime p, we prove a necessary and sufficient condition for there exists a composition {\delta} such that {\delta} can be obtained from {\lambda} after rearrangement and all the partial sums of {\delta} are…

Let $\lambda$ denote the Liouville function. We prove that $$\sum_{X \leq x < 2X} \sup_{\alpha \in \mathbb{R}/\mathbb{Z}} \bigg\lvert\!\sum_{x \leq n < x+H} \lambda(n) e(n\alpha)\bigg\rvert = o(HX)$$ as $X\to \infty$, in the regime $H =…

This paper continues the investigation begun in arXiv:1906.05602 of extending the T1 theorem of David and Journ\'e, and optimal cancellation conditions, to more general weight pairs. The main additional tool developed here is a two weight…

This paper is withdrawn because of an error in Lemma 3.1

In Theorem 1.5 of [5] an estimate from below is given for nonnegative supersolutions of parabolic equations in terms of the measure of the set where the right-hand side is less than $-1$. The given proof contains many interesting details…

We investigate the statement ``all automorphisms of $\mathcal P(\lambda)/[\lambda]^{<\lambda}$ are trivial''. We show that MA implies the statement for regular uncountable $\lambda<2^{\aleph_0}$; that the statement is false for measurable…

Our earlier publications showed semantic tableau admits partial exceptions to the Second Incompleteness Theorem where a formalism recognizes its self consistency and views multiplication as a 3-way relation (rather than as a total…

In this note, we show that a part of [5, Remark 2.2] is not correct. Some conditions are given under which the same holds.

We force $2^\lambda$ to be large and for many pairs in the interval $(\lambda,2^\lambda)$ a stronger version of the polarized partition relations hold. We apply this toproblem in general topology

Let $\phi$ be a fixed Hecke--Maass form for $\mathrm{SL}_3 (\mathbb{Z})$ and $u_j $ traverse an orthonormal basis of Hecke--Maass forms for $\mathrm{SL}_2 (\mathbb{Z}) $. Let $1/4+t_j^2$ be the Laplace eigenvalue of $u_j $. In this paper,…

Let $\Lambda$ be a quasi-tilted algebra. If $\Lambda$ is representation-finite, it was shown by Happel, Reiten, and Smal{\o} that $\Lambda$ is tilted. We provide a new, short proof of this result.