### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 123-146 |

Number of pages | 24 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 166 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2019 |

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### Cite this

*Mathematical Proceedings of the Cambridge Philosophical Society*,

*166*(1), 123-146. https://doi.org/10.1017/S0305004117000767

**Analytic number theory for 0-cycles.** / CHEN, WEIYAN.

Research output: Contribution to journal › Article

*Mathematical Proceedings of the Cambridge Philosophical Society*, vol. 166, no. 1, pp. 123-146. https://doi.org/10.1017/S0305004117000767

}

TY - JOUR

T1 - Analytic number theory for 0-cycles

AU - CHEN, WEIYAN

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.

UR - http://www.scopus.com/inward/record.url?scp=85033395775&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033395775&partnerID=8YFLogxK

U2 - 10.1017/S0305004117000767

DO - 10.1017/S0305004117000767

M3 - Article

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 -