论文标题
$ p $ - 多的任意理性维度和cantor弦的分形串
$p$-adic fractal strings of arbitrary rational dimensions and Cantor strings
论文作者
论文摘要
真实和$ p $ - adic分形弦的复杂维度的局部理论描述了振荡，这些振荡是阿基米德人和非一切内部和非一切内分形弦的几何形状，动力学和光谱的振荡。我们旨在为杜非分形弦开发一个全球复杂维度的理论，以揭示杜非分形弦的振荡性质，并从分形弦的振动和共振方面理解Riemann假设。 我们提出了一个简单而自然的构造，自然相似$ p $ - 亚法的分形弦，该链接在封闭的单位间隔$ [0,1] $中的任何理性维度。此外，作为迈向全球复杂维度理论的第一步一般的Cantor弦和AdèlicCantor String。
The local theory of complex dimensions for real and $p$-adic fractal strings describes oscillations that are intrinsic to the geometry, dynamics and spectrum of archimedean and nonarchimedean fractal strings. We aim to develop a global theory of complex dimensions for adèlic fractal strings in order to reveal the oscillatory nature of adèlic fractal strings and to understand the Riemann hypothesis in terms of the vibrations and resonances of fractal strings. We present a simple and natural construction of self-similar $p$-adic fractal strings of any rational dimension in the closed unit interval $[0,1]$. Moreover, as a first step towards a global theory of complex dimensions for adèlic fractal strings, we construct an adèlic Cantor string in the set of finite adèles $\mathbb{A}_0$ as an infinite Cartesian product of every $p$-adic Cantor string, as well as an adèlic Cantor-Smith string in the ring of adèles $\mathbb{A}$ as a Cartesian product of the general Cantor string and the adèlic Cantor string.
