The geometric sieve for densities is a very convenient tool proposed by Poonen and Stoll (and independently by Ekedahl) to compute the density of a given subset of the integers. In this paper we provide an effective criterion to find all higher moments of the density (e.g. the mean, the variance) of a subset of a finite dimensional free module over the ring of algebraic integers of a number field. More precisely, we provide a geometric sieve that allows the computation of all higher moments corresponding to the density, over a general number field
Geometric generalizations of the square sieve, with an application to cyclic covers
We formulate a general problem: Given projective schemes and over a global field
- PAR ID:
- 10401150
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Mathematika
- Volume:
- 69
- Issue:
- 1
- ISSN:
- 0025-5793
- Page Range / eLocation ID:
- p. 106-154
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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