Class Numbers of Global Function Fields

全局函数字段的类号

基本信息

  • 批准号:
    9626914
  • 负责人:
  • 金额:
    $ 6.42万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    1996
  • 资助国家:
    美国
  • 起止时间:
    1996-09-01 至 1999-08-31
  • 项目状态:
    已结题

项目摘要

Rosen 9626914 Professors Rosen and J. Hoffstein developed, some years ago, average value theorems for Dirichlet L-series formed with quadratic characters over rational function fields. Taking the special value at s=1 allows one to derive average value theorems for class numbers of hyperelliptic curves. If the constant field is a finite field with q elements, the (q-1)'st roots of unity are in the base field. If l is a prime dividing q-1, then every cyclic extension of the base field of degree l is a Kummer extension. Therefore, it seems likely that one can average Dirichlet L-series (and certain products of such series) formed with characters of order l. Also, by taking the special values at s=1, one can hope to derive class number averages as done in the quadratic case. Professor Rosen has begun work on this project and published some promising results. He will work on a number of specific problems raised by these general considerations. This research falls into the general mathematical field of Number Theory. Number theory has its historical roots in the study of the whole numbers, addressing such problems as identifying prime numbers and decomposing whole numbers as products of primes. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.
罗森9626914 几年前,罗森教授和J.霍夫斯坦教授开发了一种平均 有理函数域上由二次特征标构成的Dirichlet L-级数的值定理取s=1时的特殊值可以导出超椭圆曲线类数的平均值定理。如果常数域是一个有q个元素的有限域,则第q-1个单位根在基域中。如果l是素数整除q-1,则l次基域的每个循环扩张都是a 库默扩展。因此,似乎可以平均Dirichlet L-级数(以及此类级数的某些乘积), L阶的特征此外,通过在s=1处取特殊值,可以 希望像在二次情况下那样导出类数平均值。罗森教授已经开始了这个项目的工作,并发表了一些有希望的结果。他将研究这些一般性考虑所引起的一些具体问题。 本文的研究属于数论中的一般数学领域福尔斯。 数论的历史根源在于对整数的研究, 解决诸如识别素数和将整数分解为素数的乘积等问题。它是最古老的分支之一, 数学和追求了许多世纪纯粹的美学原因。然而,在过去的半个世纪,它已成为一个不可或缺的工具, 在诸如数据传输和处理的领域中的各种应用, 和通信系统。

项目成果

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Michael Rosen其他文献

Breakfast at Spiro's: Dramaturgy and Dominance
斯皮罗的早餐:戏剧性与统治力
  • DOI:
    10.1177/014920638501100205
  • 发表时间:
    1985
  • 期刊:
  • 影响因子:
    13.5
  • 作者:
    Michael Rosen
  • 通讯作者:
    Michael Rosen
Histopathology of the spinal cord after intrathecal cocaine, bupivacaine, lignocaine and adrenaline in the rat.
大鼠鞘内注射可卡因、布比卡因、利多卡因和肾上腺素后脊髓的组织病理学。
ANTI-TNF PHARMACOKINETICS AND RESPONSE TO THERAPY IN PEDIATRIC ACUTE SEVERE ULCERATIVE COLITIS (THE ARCH STUDY)
  • DOI:
    10.1053/j.gastro.2021.01.184
  • 发表时间:
    2021-02-01
  • 期刊:
  • 影响因子:
  • 作者:
    Kaitlin Whaley;Vivian Xiong;Rebekah Karns;Jeffrey Hyams;Subra Kugathasan;Brendan Boyle;Tom Walters;Judith Kelsen;Neal LeLeiko;Jason Shapiro;Amanda Waddell;Sejal Fox;Yael Haberman;Phillip Minar;Lee Denson;Geert D’Haens;Alexander Vinks;Michael Rosen
  • 通讯作者:
    Michael Rosen
INFLIXIMAB AND VEDOLIZUMAB HAVE SIMILAR CLINICAL AND SAFETY OUTCOMES AMONG BIOLOGIC-NAÏVE PATIENTS WITH MILD TO MODERATE PEDIATRIC INFLAMMATORY BOWEL DISEASE.
  • DOI:
    10.1053/j.gastro.2023.11.231
  • 发表时间:
    2024-02-01
  • 期刊:
  • 影响因子:
  • 作者:
    Essam Elknawy;Michael Rosen;Ruben Colman;Alka Goyal
  • 通讯作者:
    Alka Goyal
0406 : Keratinocyte-derived cardiomyocytes provide in vivo biological pacemaker function
  • DOI:
    10.1016/s1878-6480(16)30505-5
  • 发表时间:
    2016-04-01
  • 期刊:
  • 影响因子:
  • 作者:
    Samuel Chauveau;Yevgeniy Anyukhovskiy;Meital Benari;Shelly Naor;Peter Danilo;Tania Rahim;Irina Potapova;Stephanie Burke;Ya-Ping Jiang;Xiaolangshaw Qiu;Peter Brink;Binah Binah;Ira Cohen;Michael Rosen
  • 通讯作者:
    Michael Rosen

Michael Rosen的其他文献

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{{ truncateString('Michael Rosen', 18)}}的其他基金

Conference: The Lichtenbaum-Conjectures: Progress and Prospects; March, 2005; Providence, RI
会议:利希滕鲍姆猜想:进展与前景;
  • 批准号:
    0436147
  • 财政年份:
    2004
  • 资助金额:
    $ 6.42万
  • 项目类别:
    Standard Grant
Structure and Function of the Dbl Homology Domain of Human Beta-PIX, a Guanine Nucleotide Exchange Factor for the Rho GTPases
人 Beta-PIX(Rho GTP 酶的鸟嘌呤核苷酸交换因子)的 Dbl 同源结构域的结构和功能
  • 批准号:
    0296161
  • 财政年份:
    2001
  • 资助金额:
    $ 6.42万
  • 项目类别:
    Continuing Grant
Structure and Function of the Dbl Homology Domain of Human Beta-PIX, a Guanine Nucleotide Exchange Factor for the Rho GTPases
人 Beta-PIX(Rho GTP 酶的鸟嘌呤核苷酸交换因子)的 Dbl 同源结构域的结构和功能
  • 批准号:
    9817376
  • 财政年份:
    1999
  • 资助金额:
    $ 6.42万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Problems in Number Theory
数学科学:数论问题
  • 批准号:
    9209063
  • 财政年份:
    1992
  • 资助金额:
    $ 6.42万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Problems in Number Theory
数学科学:数论问题
  • 批准号:
    8903108
  • 财政年份:
    1989
  • 资助金额:
    $ 6.42万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Problems in Number Theory
数学科学:数论问题
  • 批准号:
    8606407
  • 财政年份:
    1986
  • 资助金额:
    $ 6.42万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Heegner Points on Modular Curves, Real Cyclotomic Fields, and Drinfeld Modules
数学科学:模曲线上的海格纳点、实分圆域和德林菲尔德模
  • 批准号:
    8303129
  • 财政年份:
    1983
  • 资助金额:
    $ 6.42万
  • 项目类别:
    Continuing Grant
Arithmetic of Global Function Fields
全局函数域的算术
  • 批准号:
    8103460
  • 财政年份:
    1981
  • 资助金额:
    $ 6.42万
  • 项目类别:
    Standard Grant

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  • 批准号:
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    2012
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    Standard Grant
TWC: Medium: Collaborative Proposal: Safety in Numbers: Crowdsourcing for Global Software Integrity
TWC:媒介:协作提案:数字安全:全球软件完整性的众包
  • 批准号:
    1228995
  • 财政年份:
    2012
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    $ 6.42万
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复杂射影超曲面的局部或全局特征数及其奇点的解析或改进
  • 批准号:
    15540085
  • 财政年份:
    2003
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The Formation of Large Numbers of Condensation Nuclei in Clean Global Air
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  • 批准号:
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THE FORMATION OF LARGE NUMBERS OF CONDENSATION NUCLEI IN CLEAN GLOBAL AIR
全球清洁空气中大量凝结核的形成
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    7465016
  • 财政年份:
    1974
  • 资助金额:
    $ 6.42万
  • 项目类别:
A STUDY OF THE FACTORS CONTROLLING THE FORMATION OF LARGE NUMBERS OF CONDENSATION NUCLEI IN CLEAN GLOBAL AIR
全球清洁空气中大量凝结核形成的控制因素研究
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MINIMA AND CLASS NUMBERS OF QUADRATIC FORMS OVER GLOBAL FIELDS
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    1972
  • 资助金额:
    $ 6.42万
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Minima and Class Numbers of Quadratic Forms Over Global Fields
全局域上二次型的最小值和类数
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    7204516
  • 财政年份:
    1972
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    $ 6.42万
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全球清洁空气中大量凝结核形成的控制因素研究
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