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Analytic number theory for 0-cycles

Published online by Cambridge University Press:  30 October 2017

WEIYAN CHEN
WEIYAN CHEN*
Affiliation:
Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA. e-mail: chen@math.uchicago.edu, wchen7@uchicago.edu
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Abstract

There is a well-known analogy between integers and polynomials over 𝔽q, 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 𝔽q, 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 166 , Issue 1 , January 2019 , pp. 123 - 146
Copyright
Copyright © Cambridge Philosophical Society 2017 

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