Title: On the equidistribution properties of patterns in prime numbers Jumping Champions, metaanalysis of properties as Low-Discrepancy Sequences, and some conjectures based on Ramanujan's master theorem and the zeros of Riemann's zeta function Show Chinese title

Title: 关于素数模式的等分布性质、跳跃冠军的元分析、作为低失配序列的性质，以及基于拉马努金主定理和黎曼ζ函数零点的一些猜想

Abstract: The Paul Erd\H{o}s-Tur\'an inequality is used as a quantitative form of Weyl' s criterion, together with other criteria to asses equidistribution properties on some patterns of sequences that arise from indexation of prime numbers, Jumping Champions (called here and in previous work, "meta-distances" or even md, for short). A statistical meta-analysis is also made of previous research concerning meta-distances to review the conclusion that meta-distances can be called Low-discrepancy sequences (LDS), and thus exhibiting another numerical evidence that md's are an equidistributed sequence. Ramanujan's master theorem is used to conjecture that the types of integrands where md's can be used more succesfully for quadratures are product-related, as opposite to addition-related. Finally, it is conjectured that the equidistribution of md's may be connected to the know equidistribution of zeros of Riemann's zeta function, and yet still have enough "information" for quasi-random integration ("right" amount of entropy). Show Chinese abstract

Abstract: 保罗·埃尔德什-图兰不等式被用作魏尔准则的定量形式，并与其他准则一起用于评估由素数索引生成的一些序列的均匀分布特性，这些序列被称为“跳跃冠军”（在本文和之前的工作中，也称为“元距离”或简称md）。 此外，还对关于元距离的先前研究进行了统计元分析，以审查得出结论：元距离可以被称为低失配序列（LDS），从而展示出另一个数值证据表明md是均匀分布的序列。 拉马努金主定理被用来推测，md在求积过程中能更成功使用的积分因子类型是与乘法相关的，而不是与加法相关的。 最后，推测md的均匀分布可能与黎曼ζ函数零点的已知均匀分布有关，并且仍然具有足够的“信息”来进行拟随机积分（即“恰当”的熵值）。