The Distribution of Fq-Points on Cyclic l-Covers of Genus g

被引：12

作者：

Bucur, Alina ^{[1
]}

David, Chantal ^{[2
]}

Feigon, Brooke ^{[3
,4
]}

Kaplan, Nathan ^{[5
]}

Lalin, Matilde ^{[6
]}

Ozman, Ekin ^{[7
]}

Wood, Melanie Matchett ^{[8
,9
]}

机构：

[1] Univ Calif San Diego, Dept Math, 9500 Gilman Dr 0112, La Jolla, CA 92093 USA

[2] Concordia Univ, Dept Math & Stat, 1455 de Maisonneuve West, Montreal, PQ H3G 1M8, Canada

[3] CUNY City Coll, Dept Math, NAC 8-133, New York, NY 10031 USA

[4] CUNY Grad Ctr, NAC 8-133, New York, NY 10031 USA

[5] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[6] Univ Montreal, Dept Math & Statist, CP 6128,Succ Ctr Ville, Montreal, PQ H3C 3J7, Canada

[7] Bogazici Univ, Dept Math, Fac Arts & Sci, TR-34342 Bebek, Turkey

[8] Univ Wisconsin, Dept Math, 480 Lincoln Dr, Madison, WI 53706 USA

[9] Amer Inst Math, 360 Portage Ave, Palo Alto, CA 94306 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2016年 / 2016卷 / 14期

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

DISCRIMINANTS;

D O I：

10.1093/imrn/rnv279

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study fluctuations in the number of points of l-cyclic covers of the projective line over the finite field F-q when q = 1 mod l is fixed and the genus tends to infinity. The distribution is given as a sum of q + 1 i.i.d. random variables. This was settled for hyperelliptic curves by Kurlberg and Rudnick [7], while statistics were obtained for certain components of the moduli space of l-cyclic covers in [1]. In this paper, we obtain statistics for the distribution of the number of points as the covers vary over the full moduli space of l-cyclic covers of genus g. This is achieved by relating l-covers to cyclic function field extensions, and counting such extensions with prescribed ramification and splitting conditions at a finite number of primes.

引用

页码：4297 / 4340

页数：44

共 16 条

[1] Statistics for Traces of Cyclic Trigonal Curves over Finite Fields
Bucur, Alina
David, Chantal
Feigon, Brooke
Lalin, Matilde
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2010, 2010 (05) : 932 - 967
[2] Cheong G., P AM MATH SOC
[3] Chuang C.-Y., 2015, ARXIV150901345
[4] Cohen H, 2002, J REINE ANGEW MATH, V550, P169
[5] THE DENSITY OF ABELIAN CUBIC FIELDS
COHN, H
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1954, 5 (03) : 476 - 477
[6] HAYES DR, 1974, T AM MATH SOC, V189, P77
[7] The fluctuations in the number of points on a hyperelliptic curve over a finite field
Kurlberg, Par
Rudnick, Zeev
[J]. JOURNAL OF NUMBER THEORY, 2009, 129 (03) : 580 - 587
[8] Moreno C., 1991, CAMBRIDGE TRACTS MAT, V97
[9] Rosen M.I., 2002, GRAD TEXT M, V210
[10] Traces of high powers of the Frobenius class in the hyperelliptic ensemble
Rudnick, Zeev
[J]. ACTA ARITHMETICA, 2010, 143 (01) : 81 - 99

← 1 2 →