多维复系数多项式欧拉积生成的Zeta分布
Zeta distributions generated by multidimensional polynomial Euler products with complex coefficients
摘要：
本文在${\mathbb{R}}^d$上处理了复系数的多维多项式Euler积.利用Baker定理给出了多维多项式Euler乘积生成无穷可分、拟无穷可分但非无穷可分或甚至非特征函数的充要条件.此外，我们给出了许多例子的zeta分布的${\mathbb{R}}^d$所产生的多维多项式欧拉产品与复系数。最后，我们考虑应用到解析数论。
英文摘要：
In the present paper, we treat multidimensional polynomial Euler products with complex coefficients on ${\mathbb{R}}^d$. We give necessary and sufficient conditions for the multidimensional polynomial Euler products to generate infinitely divisible, quasi-infinitely divisible but non-infinitely divisible or not even characteristic functions by using Baker's theorem. Moreover, we give many examples of zeta distributions on ${\mathbb{R}}^d$ generated by the multidimensional polynomial Euler products with complex coefficients. Finally, we consider applications to analytic number theory.
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