Statistics for biquadratic covers of the projective line over finite fields

Research output: Contribution to journalArticleScientificpeer-review

Standard

Statistics for biquadratic covers of the projective line over finite fields. / Lorenzo, Elisa; Meleleo, Giulio; Milione, Piermarco; Bucur, Alina.

In: Journal of Number Theory, Vol. 173, 2017, p. 448-477.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

APA

Vancouver

Author

Lorenzo, Elisa ; Meleleo, Giulio ; Milione, Piermarco ; Bucur, Alina. / Statistics for biquadratic covers of the projective line over finite fields. In: Journal of Number Theory. 2017 ; Vol. 173. pp. 448-477.

Bibtex - Download

@article{6db6297e659549518758983cdc3898c0,
title = "Statistics for biquadratic covers of the projective line over finite fields",
abstract = "We study the distribution of the traces of the Frobenius endomorphisms of genus g curves which are quartic non-cyclic covers of View the MathML sourcePFq1, as the curve varies in an irreducible component of the moduli space. We show that for q fixed, the limiting distribution of the traces of Frobenius equals the sum of q+1q+1 independent random discrete variables. We also show that when both g and q go to infinity, the normalized trace has a standard complex Gaussian distribution. Finally, we extend these computations to the general case of arbitrary covers of View the MathML sourcePFq1 with Galois group isomorphic to r copies of Z/2ZZ/2Z. For r=1r=1 we recover the already known results for the family of hyperelliptic curves.",
keywords = "Function fields, Biquadratic curves, Biquadratic covers, Number of points over finite fields, Arithmetic statistics",
author = "Elisa Lorenzo and Giulio Meleleo and Piermarco Milione and Alina Bucur",
year = "2017",
doi = "10.1016/j.jnt.2016.09.007",
language = "English",
volume = "173",
pages = "448--477",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press Inc.",

}

RIS - Download

TY - JOUR

T1 - Statistics for biquadratic covers of the projective line over finite fields

AU - Lorenzo, Elisa

AU - Meleleo, Giulio

AU - Milione, Piermarco

AU - Bucur, Alina

PY - 2017

Y1 - 2017

N2 - We study the distribution of the traces of the Frobenius endomorphisms of genus g curves which are quartic non-cyclic covers of View the MathML sourcePFq1, as the curve varies in an irreducible component of the moduli space. We show that for q fixed, the limiting distribution of the traces of Frobenius equals the sum of q+1q+1 independent random discrete variables. We also show that when both g and q go to infinity, the normalized trace has a standard complex Gaussian distribution. Finally, we extend these computations to the general case of arbitrary covers of View the MathML sourcePFq1 with Galois group isomorphic to r copies of Z/2ZZ/2Z. For r=1r=1 we recover the already known results for the family of hyperelliptic curves.

AB - We study the distribution of the traces of the Frobenius endomorphisms of genus g curves which are quartic non-cyclic covers of View the MathML sourcePFq1, as the curve varies in an irreducible component of the moduli space. We show that for q fixed, the limiting distribution of the traces of Frobenius equals the sum of q+1q+1 independent random discrete variables. We also show that when both g and q go to infinity, the normalized trace has a standard complex Gaussian distribution. Finally, we extend these computations to the general case of arbitrary covers of View the MathML sourcePFq1 with Galois group isomorphic to r copies of Z/2ZZ/2Z. For r=1r=1 we recover the already known results for the family of hyperelliptic curves.

KW - Function fields

KW - Biquadratic curves

KW - Biquadratic covers

KW - Number of points over finite fields

KW - Arithmetic statistics

U2 - 10.1016/j.jnt.2016.09.007

DO - 10.1016/j.jnt.2016.09.007

M3 - Article

VL - 173

SP - 448

EP - 477

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -

ID: 11678241