Analytic number theory for 0-cycles
Analytic number theory for 0-cycles
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0 循环的解析数论
DOI：
10.1017/s0305004117000767
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发表时间：
2016
影响因子：
0.8
通讯作者：
Weiyan Chen
中科院分区：
文献类型：
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作者：
Weiyan Chen
整数和多项式之间有一个众所周知的类比。Q，以及大量关于多项式解析数论的文献。从几何角度看，多项式等价于仿射线上的有效0环。这让人不禁要问：整数和多项式之间的类比是否可以扩展到更一般的变量上的0环？本文研究了任意连通变量V / ?上有效0环的素分解问题。Q，强调整数和0环之间的类比。例如，受Granville和Rhoades的启发，我们证明了0环的素数因子是典型的泊松分布。
Abstract There is a well-known analogy between integers and polynomials over ?q, and a vast literature on analytic number theory for polynomials. From a geometric point of view, polynomials are equivalent to effective 0-cycles on the affine line. This leads one to ask: Can the analogy between integers and polynomials be extended to 0-cycles on more general varieties? In this paper we study prime factorisation of effective 0-cycles on an arbitrary connected variety V over ?q, emphasizing the analogy between integers and 0-cycles. For example, inspired by the works of Granville and Rhoades, we prove that the prime factors of 0-cycles are typically Poisson distributed.