Arithmetic Statistics: Groups of Elliptic Curves and Abelian Varieties, and Zeroes of Families of Curves over Finite Fields.
算术统计:椭圆曲线群和阿贝尔簇,以及有限域上曲线族的零点。
基本信息
- 批准号:155635-2013
- 负责人:
- 金额:$ 1.68万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2017
- 资助国家:加拿大
- 起止时间:2017-01-01 至 2018-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This research proposal is concerned with Arithmetic Statistics, a new branch of numbertheory which emerged from the spectacular new developments of the last decadesabout distribution questions related to number theoritic objects. The two maindistribution questions that we are investigating are:(1)If we look at a random sequence of groups,such as class groups of quadratic imaginary extensions, or groups ofpoints of elliptic curves over finite fields, how are those groups distributed?A naive probabilistic model would be that groups of the same size are uniformlydistributed, but strong evidence indicates that the probability is inversely proportional to the size of the automorphism group, as predicted by the Cohen-Lenstra heuristics.(2) What are the statistics for the distribution of the number of points in families of curves over finite fields? When studying this variation in families where the size of the finite field gets large, the distribution is coming from random matrix theory as proven by Katz and Sarnak. By contrast, there is no general conjectural picture of what one should expect for the study of families at the large genus limit when the size of the finite field.
本研究计划涉及算术统计学,这是数论的一个新的分支,它产生于过去几十年有关数论对象的分布问题的引人注目的新发展。我们正在研究的两个主要分布问题是:(1)如果我们看一个随机的群序列,如二次虚扩张的类群,或有限域上椭圆曲线的点群,这些群是如何分布的?一个简单的概率模型是相同大小的组是均匀分布的,但强有力的证据表明,概率与自同构组的大小成反比,正如科恩-伦斯特拉统计学所预测的那样。(2)有限域上曲线族中点的数目分布的统计量是什么?当研究有限域的大小变大的家庭中的这种变化时,分布来自Katz和Sarnak证明的随机矩阵理论。相比之下,当有限域的大小达到大亏格极限时,对于族的研究,人们应该期望什么,并没有一个普遍的理论图景。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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David, Chantal其他文献
On the vanishing of twisted L-functions of elliptic curves over rational function fields
关于有理函数域上椭圆曲线扭曲L函数的消失
- DOI:
10.1007/s40993-022-00379-w - 发表时间:
2022 - 期刊:
- 影响因子:0.8
- 作者:
Comeau-Lapointe, Antoine;David, Chantal;Lalin, Matilde;Li, Wanlin - 通讯作者:
Li, Wanlin
Use of Flow Modeling to Optimize the Twin-Screw Extrusion Process for the Preparation of Lignocellulosic Fiber-Based Composites
- DOI:
10.3389/fmats.2020.00218 - 发表时间:
2020-07-24 - 期刊:
- 影响因子:3.2
- 作者:
Berzin, Francoise;David, Chantal;Vergnes, Bruno - 通讯作者:
Vergnes, Bruno
Modelling and Validation of Synthesis of Poly Lactic Acid Using an Alternative Energy Source through a Continuous Reactive Extrusion Process
- DOI:
10.3390/polym8040164 - 发表时间:
2016-04-01 - 期刊:
- 影响因子:5
- 作者:
Dubey, Satya P.;Abhyankar, Hrushikesh A.;David, Chantal - 通讯作者:
David, Chantal
Non-isotrivial elliptic surfaces with non-zero average root number
平均根数非零的非等平凡椭圆面
- DOI:
10.1016/j.jnt.2018.03.007 - 发表时间:
2018 - 期刊:
- 影响因子:0.7
- 作者:
Bettin, Sandro;David, Chantal;Delaunay, Christophe - 通讯作者:
Delaunay, Christophe
Microwave energy assisted synthesis of poly lactic acid via continuous reactive extrusion: modelling of reaction kinetics
- DOI:
10.1039/c6ra26514f - 发表时间:
2017-01-01 - 期刊:
- 影响因子:3.9
- 作者:
Dubey, Satya P.;Abhyankar, Hrushikesh A.;David, Chantal - 通讯作者:
David, Chantal
David, Chantal的其他文献
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{{ truncateString('David, Chantal', 18)}}的其他基金
L-functions over number fields and function fields
数域和函数域上的 L 函数
- 批准号:
RGPIN-2019-05536 - 财政年份:2022
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
L-functions over number fields and function fields
数域和函数域上的 L 函数
- 批准号:
RGPIN-2019-05536 - 财政年份:2021
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
L-functions over number fields and function fields
数域和函数域上的 L 函数
- 批准号:
RGPIN-2019-05536 - 财政年份:2020
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
L-functions over number fields and function fields
数域和函数域上的 L 函数
- 批准号:
RGPIN-2019-05536 - 财政年份:2019
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Arithmetic Statistics: Groups of Elliptic Curves and Abelian Varieties, and Zeroes of Families of Curves over Finite Fields.
算术统计:椭圆曲线群和阿贝尔簇,以及有限域上曲线族的零点。
- 批准号:
155635-2013 - 财政年份:2018
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Arithmetic Statistics: Groups of Elliptic Curves and Abelian Varieties, and Zeroes of Families of Curves over Finite Fields.
算术统计:椭圆曲线群和阿贝尔簇,以及有限域上曲线族的零点。
- 批准号:
155635-2013 - 财政年份:2015
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Arithmetic Statistics: Groups of Elliptic Curves and Abelian Varieties, and Zeroes of Families of Curves over Finite Fields.
算术统计:椭圆曲线群和阿贝尔簇,以及有限域上曲线族的零点。
- 批准号:
155635-2013 - 财政年份:2014
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Arithmetic Statistics: Groups of Elliptic Curves and Abelian Varieties, and Zeroes of Families of Curves over Finite Fields.
算术统计:椭圆曲线群和阿贝尔簇,以及有限域上曲线族的零点。
- 批准号:
155635-2013 - 财政年份:2013
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Elliptic curves and L-functions
椭圆曲线和 L 函数
- 批准号:
155635-2008 - 财政年份:2012
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Elliptic curves and L-functions
椭圆曲线和 L 函数
- 批准号:
155635-2008 - 财政年份:2011
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
相似海外基金
Arithmetic Statistics: Asymptotics on number fields and their class groups
算术统计:数域及其类群的渐近
- 批准号:
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Selmer 群、算术统计和宇称猜想。
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- 批准号:
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算术统计:数域及其类群的渐近
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Arithmetic Statistics: Asymptotics on number fields and their class groups
算术统计:数域及其类群的渐近
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Arithmetic Statistics: Groups of Elliptic Curves and Abelian Varieties, and Zeroes of Families of Curves over Finite Fields.
算术统计:椭圆曲线群和阿贝尔簇,以及有限域上曲线族的零点。
- 批准号:
155635-2013 - 财政年份:2018
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Arithmetic Statistics: Groups of Elliptic Curves and Abelian Varieties, and Zeroes of Families of Curves over Finite Fields.
算术统计:椭圆曲线群和阿贝尔簇,以及有限域上曲线族的零点。
- 批准号:
155635-2013 - 财政年份:2015
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Arithmetic Statistics: Groups of Elliptic Curves and Abelian Varieties, and Zeroes of Families of Curves over Finite Fields.
算术统计:椭圆曲线群和阿贝尔簇,以及有限域上曲线族的零点。
- 批准号:
155635-2013 - 财政年份:2014
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual
Arithmetic Statistics: Groups of Elliptic Curves and Abelian Varieties, and Zeroes of Families of Curves over Finite Fields.
算术统计:椭圆曲线群和阿贝尔簇,以及有限域上曲线族的零点。
- 批准号:
155635-2013 - 财政年份:2013
- 资助金额:
$ 1.68万 - 项目类别:
Discovery Grants Program - Individual