TY - JOUR
T1 - Analytic number theory for 0-cycles
AU - CHEN, WEIYAN
N1 - Publisher Copyright:
Copyright © 2017 Cambridge Philosophical Society.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - There is a well-known analogy between integers and polynomials over F 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 F 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.
AB - There is a well-known analogy between integers and polynomials over F 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 F 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.
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U2 - 10.1017/S0305004117000767
DO - 10.1017/S0305004117000767
M3 - Article
AN - SCOPUS:85033395775
VL - 166
SP - 123
EP - 146
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
SN - 0305-0041
IS - 1
ER -