论文标题
根据素数定义的某些功能的有效估计
Effective estimates for some functions defined over primes
论文作者
论文摘要
在本文中，我们对根据质数定义的某些经典算术功能进行有效的估计。首先，我们找到了最小的实际数字$ x_0 $，因此每$ x \ geq x_0 $都可以容纳涉及Chebyshev $ \ vartheta $ function的某些不平等。然后，我们在短时间间隔中给出了一些有关质数存在的新结果。另外，我们为某些在质数上定义的函数（例如素数函数$π（x）$）得出了新的上限和下限，从而改善了相似形状的当前最佳估计。
In this paper we give effective estimates for some classical arithmetic functions defined over prime numbers. First we find the smallest real number $x_0$ so that some inequality involving Chebyshev's $\vartheta$-function holds for every $x \geq x_0$. Then we give some new results concerning the existence of prime numbers in short intervals. Also we derive new upper and lower bounds for some functions defined over prime numbers, for instance the prime counting function $π(x)$, which improve current best estimates of similar shape.
