相关论文: An improvement of Zalcman's lemma in $C^n$

In the present note a generalization of Borel-Cantelli Lemma is proposed.

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

In this paper, as an application of Zalcman's lemma in $\mathbb{C}^n$, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J.…

We give an estimate of the growth of a polynonial mapping of $C^n$.

Extending the idea in [Impagliazzo, R., Moore, C. and Russell, A., An entropic proof of Chang's inequality. SIAM Journal on Discrete Mathematics, 28(1), pp.173-176.] we give a short information theoretic proof for Chang's lemma that is…

In this paper we prove a Schwarz-Pick lemma for bounded complex-valued harmonic functions in the unit ball of R^n.

Based on new explicit estimates for the prime counting function, we improve the currently known estimates for the particular sequence $C_n = np_n - \sum_{k \leq n}p_k$, $n \geq 1$, involving the prime numbers.

We prove a variation of Gronwall's lemma.

In this paper we calculate the collection of limit functions obtained by applying an extension of Zalcman's Lemma, due to X. C. Pang, to the non-normal family $\left\{f(nz):n\in\mathbb{N}\right\}$ in $\mathbb{C}$, where $f=Re^P$. Here $R$…

The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

In this paper, we prove that the discrete Copson inequality (E.T. Copson, \emph{Notes on a series of positive terms}, J. London Math. Soc., 2 (1927), 49-51) of one-dimension in general cases admits an improvement. In fact we study the…

The paper is devoted to the problem of estimating the constant of the best Diophantine approximations. The estimates of lower bound $ C_n $ for $ n = 5 $ and $ n = 6 $ was improved. The first chapter gives an overview of the history of…

Remarks on the Obstructedness of Cones Over Curves of Low Genus. Reason for replacement: proof of the main lemma was significantly improved.

In this short note we have proved an enhanced version of a theorem of Lorentz [1] and its generalization to the multivariate case which gives a non- uniform estimate of degree of approximation by a polynomial with positive coefficients. The…

This was originally an appendix to our paper `Fourier expansions at cusps' [arXiv:1807.00391]. The purpose of this note is to give a proof of a theorem of Shimura on the action of $\mathrm{Aut}(\mathbb{C})$ on modular forms for $\Gamma(N)$…

We present inequalities and some applications to Kellers' limit and Carlemans' inequality.

In this article we propose a revisitation of the well-known argument principle that may lead to the solution of the Riemann hypothesis. We are looking for collaborators.

In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.

The purpose of this paper is to provide a random version of Simons' inequality.