论文标题
谐波数量和素数功能
Harmonic numbers and the prime counting function
论文作者
论文摘要
我们通过各种离散版本的对数积分函数提供了质量计数函数的近似值，该函数仅以谐波数来表示。我们用明确的误差界证明这些近似值至少与对数积分近似值一样好。作为推论，我们根据质量计数函数和谐波数来对Riemann假设进行一些重新阐述。
We provide approximations to the prime counting function by various discretized versions of the logarithmic integral function, expressed solely in terms of the harmonic numbers. We demonstrate with explicit error bounds that these approximations are at least as good as the logarithmic integral approximation. As a corollary, we provide some reformulations of the Riemann hypothesis in terms of the prime counting function and the harmonic numbers.
