A heuristic for the distribution of point counts for random curves over a finite field.
Philos Trans A Math Phys Eng Sci
; 239(2040)2015 Apr 28.
Article
em En
| MEDLINE
| ID: mdl-25802415
ABSTRACT
How many rational points are there on a random algebraic curve of large genus g over a given finite field Fq? We propose a heuristic for this question motivated by a (now proven) conjecture of Mumford on the cohomology of moduli spaces of curves; this heuristic suggests a Poisson distribution with mean q+1+1/(q-1). We prove a weaker version of this statement in which g and q tend to infinity, with q much larger than g.
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Coleções:
01-internacional
Base de dados:
MEDLINE
Tipo de estudo:
Clinical_trials
Idioma:
En
Ano de publicação:
2015
Tipo de documento:
Article