论文标题
关于素数和黎曼零
On Prime Numbers and The Riemann Zeros
论文作者
论文摘要
有关Riemann零的当前研究表明，在Riemann Zeros集中存在非平凡的代数/分析结构。 Primes和Riemann Zeta函数零之间的二元性表明要研究的一些新目标和方面：{\ em adelic duality}和峰值数字的{\ em poset}。 本文提供了Riemann Zeta函数的非平凡零零零零零件的结构的计算证据$ρ= 1/2+IT $，在本文中称为{\ em em riemann spectrum}，使用其分布研究。 新颖性代表着考虑相关字符$ p^{it} $，即代数观点，而不是从分析数理论的意义上。这种结构是根据阿德式特征和理性的双重性来解释的。 其次，所研究的质数的POSET结构是通过二元性在Riemann Spectrum中进行偶然反映的。提出了对沿着普拉特树的傅立叶系列收敛性的直接研究。 以下是探索以下考虑的考虑因素，以Hecke Idelic字符，本地Zeta积分（Mellin Transform）和$ω$ -EIGEN-DISTRICTIONS相关联。
The current research regarding the Riemann zeros suggests the existence of a non-trivial algebraic/analytic structure on the set of Riemann zeros. The duality between primes and Riemann zeta function zeros suggests some new goals and aspects to be studied: {\em adelic duality} and the {\em POSet of prime numbers}. The article presents computational evidence of the structure of the imaginary parts $t$ of the non-trivial zeros of the Riemann zeta function $ρ=1/2+it$, called in this article the {\em Riemann Spectrum}, using the study of their distribution. The novelty represents in considering the associated characters $p^{it}$, towards an algebraic point of view, than rather in the sense of Analytic Number Theory. This structure is tentatively interpreted in terms of adelic characters, and the duality of the rationals. Second, the POSet structure of prime numbers studied, is tentatively mirrored via duality in the Riemann spectrum. A direct study of the convergence of their Fourier series, along Pratt trees, is proposed. Further considerations, relating the Riemann Spectrum, adelic characters and distributions, in terms of Hecke idelic characters, local zeta integrals (Mellin transform) and $ω$-eigen-distributions, are explored following.
