素数同态、丢番图方程和黎曼假设
Prime Number Diffeomorphisms, Diophantine Equations and the Riemann Hypothesis
摘要：
我们用适当的二次样条插值素级数来显式地构造一个双纯对（p（x），p^{-1}（x））.这些连续可微函数分别是素数级数和素数计数函数的光滑模拟，包含了素数特定行为的基本信息。我们使用p^{-1}（x）来找到素数上丢番图方程的近似解，并讨论如何使用这个函数来分析素数定理中的误差的von Koch估计，该定理与黎曼假设是等价的。
英文摘要：
We explicitly construct a diffeomorphic pair (p(x),p^{-1}(x)) in terms of an appropriate quadric spline interpolating the prime series. These continuously differentiable functions are the smooth analogs of the prime series and the prime counting function, respectively, and contain the basic information about the specific behavior of the primes. We employ p^{-1}(x) to find approximate solutions of Diophantine equations over the primes and discuss how this function could eventually be used to analyze the von Koch estimate for the error in the prime number theorem which is known to be equivalent to the Riemann hypothesis.
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。
