高斯、赫维茨、屋大维和爱森斯坦素数的哥德巴赫
Goldbach for Gaussian, Hurwitz, Octavian and Eisenstein primes
摘要：
我们制定哥德巴赫型问题的高斯，赫维茨，屋大维和爱森斯坦素数。它们不同于1960年以来三井隆吉对数域或CA的哥德巴赫型陈述。Holben和James Jordan在1968年提出了高斯整数。1）满足a>2，b>2的偶数高斯整数a+ib是两个正系数高斯素数之和。2)每个Eisenstein整数a+bw（a>3，b>3，w=（1+sqrt（-3））/2）是两个正系数Eisenstein素数之和.注意，在爱森斯坦的情况下没有要求均匀性条件。3)每个Lipschitz正整数四元数都是两个Hurwitz素数之和。4)存在一个常数K，使得每个系数大于K的Octavian整数都是两个Octavian素数之和。除了在八元数的情况下，在那里做了最少的实验，这些陈述可以联系到困难的问题，如朗道或布尼亚科夫斯基命题。因此，我们也更仔细地和数字地研究了一些哈迪-利特尔伍德常数，这些常数是在50年代和70年代丹尼尔·尚克斯和马文·温德利希的早期计算之后得出的。
英文摘要：
We formulate Goldbach type questions for Gaussian, Hurwitz, Octavian and Eisenstein primes. They are different from Goldbach type statements by Takayoshi Mitsui from 1960 for number fields or C.A. Holben and James Jordan from 1968 for Gaussian integers. Here is what we meeasure: 1) Every even Gaussian integer a+ib satisfying a>2, b>2 is a sum of two Gaussian primes with positive coefficients. 2) Every Eisenstein integer a+bw with a>3,b>3 and w=(1+sqrt(-3))/2 is the sum of two Eisenstein primes with positive coefficients. Note that no evenness condition is asked in the Eisenstein case. 3) Every Lipschitz integer quaternion with positive entries is the sum of two Hurwitz primes. 4) There exists a constant K such that every Octavian integer with coefficients larger than K is the sum of two Octavian primes. Except in the Octonion case, where the fewest experiments were done, the statements can be linked to difficult questions like Landau or Bunyakovsky conjectures. We therefore look also more closely and numerically at some Hardy-Littlewood constants following early computations from Daniel Shanks and Marvin Wunderlich from the 50ies and 70ies.
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。
