论文标题
Prime产品的特性和Robin的不平等
Properties of Prime Products and Robin's Inequality
论文作者
论文摘要
事实证明，有许多问题与现代数学中的Riemann假设相同。在本文中，我们探讨了1984年罗宾（Robin）在1984年得出的不平等的表述，当时且仅当罗宾（Robin）的不平等对所有$ n \ geq 5040 $都是正确时，就证明了Riemann假设为True。在本文中，我们查看了质数的显式产品，并表明，如果给定的$ n = p_1^{k_1} p_2^{k_2} {k_2} \ ldots p_m^{k_m} $满足罗宾的不平等，那么$ n = p_1^{k_1} p_1} p_1} p_2^$ ______________________________ p_m^\ ldots p_m^\ ldots p_m^\ ldots p_m^\ ldots p_m^\ ldots p_m^\ ldots p_m^\ ldots p_m。 \ leq p_j $也满足不平等。然后，我们还提供了两个猜想，如果证明单独可以暗示Riemann假设和Robin不平等的一些有趣的特性。
There are many formulations of problems that have been proven to be equivalent to the Riemann Hypothesis in modern mathematics. In this paper we look at the formulation of an inequality derived by Robin in 1984 that proves the Riemann Hypothesis true if and only if Robin's Inequality is true for all $n\geq 5040$. In this paper we look at explicit products of prime numbers and show that if a given $n=p_1^{k_1}p_2^{k_2}\ldots p_m^{k_m}$ satisfies Robin's Inequality, then $n=P_1^{k_1}P_2^{k_2}\ldots P_m^{k_m}$ with $p_j \leq P_j$ also satisfies the inequality. We also then offer two conjectures that if proven individually could imply some interesting properties of the Riemann Hypothesis and Robin's Inequality.
