超过剩数、超过剩性与黎曼假设
Superabundant numbers, their subsequences and the Riemann hypothesis
摘要：
设σ（n）是正整数n的约数之和。罗宾定理指出，黎曼假设等价于不等式σ（n）<e^γn \log \log n对于所有n>5040（γ是欧拉常数）。这是一个自然的问题，在这个方向上找到第一个整数，如果存在，这违反了这个不等式。在这个过程之后，我们引入了一个新的数列，并称之为极丰富数。本文证明了黎曼假设成立的充要条件是存在无穷多个这样的数。此外，我们还研究了它们的一些性质以及超富足数和泛富足数。
英文摘要：
Let σ(n) be the sum of divisors of a positive integer n. Robin's theorem states that the Riemann hypothesis is equivalent to the inequality σ(n)<e^γn\log\log n for all n>5040 (γis Euler's constant). It is a natural question in this direction to find a first integer, if exists, which violates this inequality. Following this process, we introduce a new sequence of numbers and call it as extremely abundant numbers. In this paper we show that the Riemann hypothesis is true, if and only if, there are infinitely many of these numbers. Moreover, we investigate some of their properties together with superabundant and colossally abundant numbers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
