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

This paper contains a small improvement to the explicit bounds on the growth of the function $S(T)$. It is shown how more substantial improvements are possible if one has better explicit bounds on the growth of $|\zeta(\frac{1}{2}+it)|$.

We give arguments for and prove the consistency of some internal forcing axioms.

Some occurrences of $n$ can be replaced by $n-1$ in a special case of the Shapley-Folkman lemma.

In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.

In the paper based on the question of Zhang and L\"{u}[15], we present one theorem which will improve and extend the results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

In this paper we provide an application to the Neumann problem of a recent three critical points theorem.

We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.

In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.

In comparison with the previous version of this paper, the Introduction is slightly changed and some minor typos are deleted. All results are unchanged.

We give a complete self-contained proof of Statman's finite completeness theorem and of a corollary of this theorem stating that the $\lambda$-definability conjecture implies the higher-order matching conjecture.

We prove an approximation theorem on a class of domains in $\mathbb{C}^n$ on which the $\overline{\partial}$-problem is solvable in $L^{\infty}$. Furthermore, as a corollary, we obtain a version of the Axler-\v{C}u\v{c}kovi\'c-Rao Theorem…

We explain the Elekes Szabo paper in more details and improve the constant in one dimensional case in \mathbb{R} and \mathbb{C}.

In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.

We improve an isoperimetric inequality due to Panos Papasoglu. We also generalize this inequality to the Finsler case by proving an optimal Finsler version of the Besicovitch's lemma which holds for any notion of Finsler volume.

We give new lower asymptotical estimate of constant \[ C_n=\sup\biggl\{\frac{\|t_n\|_{C(\mathbb T)}}{\|t_n\|_{L(\mathbb T)}}:t_n\text{are real trigonometric polynomials}, \operatorname{deg}t_n<n\biggr\} \] as $n\to\infty$. This estimate…

In classical estimation theory, the central limit theorem implies that the statistical error in a measurement outcome can be reduced by an amount proportional to n^(-1/2) by repeating the measures n times and then averaging. Using quantum…

We present a survey on recent results about Stirling's formula. More exactly, we reffer to a method using a form of Cesaro-Stolz lemma firstly introduced in [C. Mortici Product approximations via asymptotic integration Amer. Math. Monthly…

In this short note, we employ well-known results to improve the lower bound for the constant associated with the linear term in the asymptotic expansion of the minimal logarithmic energy on the sphere.

The purpose of this note is to improve the current theoretical results for the correlation functions of the Mobius sequence $\{\mu(n): n\geq 1 \}$ and the Liouville sequence $\{\lambda(n): n\geq 1 \}$.