论文标题
Furstenberg的无限级定理的扩展
An extension of Furstenberg's theorem of the infinitude of primes
论文作者
论文摘要
$ \ mathbb {z} $上的常规产品$ m \ cdot n $可以看作是算术进程的$ n $项的总和，其第一项为$ a_ {1} = m-n+1 $，其差额为$ d = 2 $。概括这个想法，我们定义了新的类似的产品映射，并考虑了新的算术，使我们能够扩展Furstenberg的无限量学定理。我们还回顾了新算术中的经典猜想。最后，我们对主要思想进行了重要的扩展。我们看到，给定任何整数序列，该方法在整数上生成算术，并且与$ \ Mathbb {z} \ setMinus \ { - 1,1 \} $相似的公式。
The usual product $m\cdot n$ on $\mathbb{Z}$ can be viewed as the sum of $n$ terms of an arithmetic progression whose first term is $a_{1}=m-n+1$ and whose difference is $d=2$. Generalizing this idea, we define new similar product mappings, and we consider new arithmetics that enable us to extend Furstenberg's theorem of the infinitude of primes. We also review the classic conjectures in the new arithmetics. Finally, we make important extensions of the main idea. We see that given any integer sequence, the approach generates an arithmetic on integers and a similar formula to $\mathbb{Z} \setminus \{-1,1\}$ arises.
