论文标题
Chebyshev反对全球领域的分裂和主要素数的偏见
Chebyshev's Bias against Splitting and Principal Primes in Global Fields
论文作者
论文摘要
调查了Chebyshev偏见出现的原因。 Riemann Deep Hoseases（DRH）使我们能够揭示偏见是实现整个Prime平衡处置的自然现象，从某种意义上说，Euler产品在中心会收敛。通过素数的加权计数函数，作者成功地在DRH的假设下通过某个渐近公式表达了偏转的幅度，该公式提供了Chebyshev偏见的新表述。对于Galois集团中全球田地和任何元素$σ$的任何GALOIS扩展，我们已经建立了在DRH假设下的frobenius元素等于$σ$的质数的标准。作为应用程序，我们已经在DRH下的Abelian扩展中获得了非分类和非原则的偏见。在积极的特征情况下，DRH是已知的，所有这些结果无条件地成立。
Reasons for the emergence of Chebyshev's bias were investigated. The Deep Riemann Hypothesis (DRH) enables us to reveal that the bias is a natural phenomenon for achieving a well-balanced disposition of the whole sequence of primes, in the sense that the Euler product converges at the center. By means of a weighted counting function of primes, the authors succeed in expressing magnitudes of the deflection by a certain asymptotic formula under the assumption of DRH, which provides a new formulation of Chebyshev's bias. For any Galois extension of global fields and for any element $σ$ in the Galois group, we have established a criterion of the bias of primes whose Frobenius elements are equal to $σ$ under the assumption of DRH. As an application we have obtained a bias toward non-splitting and non-principle primes in abelian extensions under DRH. In positive characteristic cases, DRH is known, and all these results hold unconditionally.
