论文标题
多项式和多个Dedekind Zeta函数代表的素数分布
Distribution of primes represented by polynomials and Multiple Dedekind zeta functions
论文作者
论文摘要
在本文中，我们陈述了有关素数的分布以及在两个变量$ f（a，b）$中以不可约均质多项式代表的素数分布的几种猜想。对于任何不可约多项式$ f $，我们就斜率$ t = b/a $提出了猜想。在这里，我们为所有不可约多项式制定了一个猜想。 我们还考虑了分配成对素数的猜想。它显示出与多个Dedekind Zeta函数的意外关系 - $ s = 2 $，一个prime和$（s_1，s_2）=（2,2）$的prime。我们测试了几个二次场的素数的猜想。高斯整数上的成对素数和多个Dedekind Zeta函数的猜想提供的误差不到百分之十的十分之一。 我们还测试了比较一对不同二次场中素数集的猜想。从数字上讲，这些商可以用调节器和班级数来表示。 某些数据以及代码可在GitHub上获得（请参阅\ cite {zouberou}）。
n this paper, we state several conjectures regarding distribution of primes and of pairs of primes represented by irreducible homogeneous polynomial in two variables $f(a,b)$. We formulate conjectures with respect to the slope $t=b/a$ for any irreducible polynomial $f$. Here, we formulate a conjecture for all irreducible polynomials. We also consider conjectures for distribution of pairs of primes. It show unexpected relation to multiple Dedekind zeta function - at $s=2$ for one prime and at $(s_1,s_2)=(2,2)$ for pairs of primes. We tested the conjecture for pairs of primes for several quadratic fields. The conjecture for pairs of primes and multiple Dedekind zeta function over the Gaussian integers provide error less than a tenth of a percent. We also tested conjectures that compare sets of primes in a pair of different quadratic fields. Numerically, such quotients can be expressed in terms of regulators and class numbers. Some of the data, together with the code, is available on GitHub, (see \cite{Zouberou}).
