受Erdős启发的一个不等式

另一个受埃罗什启发的不等式

Another inequality inspired by Erdős

本文通过算术方法研究并解决了一个受埃罗什经典证明启发的正整数不等式，旨在寻找伯特兰公式的纯算术证明。

Alladi、Erdös和Vaaler不等式的改进平均界

Improved Average Bounds for an Inequality of Alladi, Erdös, and Vaaler

本文证明了Alladi、Erdös和Vaaler猜想的一个平均版本，表明满足特定大小约束的乘性函数的除数和大部分值来源于其“小”除数。

A hybrid inequality of Erdös-Turán-Koksma for digital sequences

For bases $\mathbf{b}=(b_1,..., b_s)$ of $s$ not necessarily distinct integers $b_i\ge 2$, we prove a version of the inequality of \etk \ for the hybrid function system composed of the Walsh functions in base $\bfb^{(1)}=(b_1,..., b_{s_1})$ and, as second component, the $\bfb^{(2)}$-adic functions, $\bfb^{(2)}=(b_{s_1+1},..., b_s)$, with $s=s_1+s_2$, $s_1$ and $s_2$ not both equal to 0. Further, we point out why this choice of a hybrid function system covers all possible cases of sequences that employ addition of digit vectors as their main construction principle.

The Sharp Erdős-Turán Inequality

Erdős and Turán proved a classical inequality on the distribution of roots for a complex polynomial in 1950, depicting the fundamental interplay between the size of the coefficients of a polynomial and the distribution of its roots on the complex plane. Various results have been dedicated to improving the constant in this inequality, while the optimal constant remains open. In this paper, we give the optimal constant, i.e., prove the sharp Erdős-Turán inequality. To achieve this goal, we reformulate the inequality into an optimization problem, whose equilibriums coincide with a class of energy…

Trigonometric approximation and a general form of the Erdős Turán inequality

There exists a positive function $ψ(t)${on}$t\geq0${, with fast decay at infinity, such that for every measurable set}$Ω${in the Euclidean space and}$R>0${, there exist entire functions}$A(x) ${and}$B(x) ${of exponential type}$R${, satisfying\}$A(x)\leq χ_Ω(x)\leq B(x)${and}$| B(x)-A(x)| \leqslantψ(R\operatorname*{dist}(x,\partialΩ)) $. This leads to Erdős Turán estimates for discrepancy of point set distributions in the multi dimensional torus. Analogous results hold for approximations by eigenfunctions of differential operators and discrepancy on compact manifolds.

原始集合的Erdős不等式

Erdős inequality for primitive sets

本文将Erdős关于原始集合的经典不等式从z=1推广到z∈(0,2)，并研究z趋于0时的极限及特定集合的渐近展开。