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Mathematical Sciences: Multiplicity One Results for Automorphic Forms via L-functions

Mathematical Sciences: Multiplicity One Results for Automorphic Forms via L-functions
数学科学:通过 L 函数得出自同构形式的重数一结果
批准号:
9501151
负责人:
Dinakar Ramakrishnan
金额:
$9.45万
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
1995
资助国家:
美国
项目状态:
已结题
起止时间:
1995-07-15 至 1998-12-31

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中文摘要
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英文摘要
This award supports the research of Professor Dinakar Ramakrishnan in the theory of automorphic forms and representations. This work involves three problems with relations to number theory, which have L-functions as a common theme. The main focus is on a program to prove multiplicity one for the space of cusp forms on the special linear group SL(2). The second problem concerns fine versions of the strong multiplicity one theorem for the general linear group GL(n). Finally, the principal investigator seeks to complete a proof of the Tate conjecture for all quaternionic Shimura surfaces. Historically, automorphic forms arose out of non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.
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Modular varieties, arithmetic and geometry
  • 批准号:
    1001916
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $30.91万
  • 财政年份:
    2010
  • 负责人:
    Dinakar Ramakrishnan
  • 依托单位:
Automorphic Forms, and their links to Arithmetic and Geometry
  • 批准号:
    0701089
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $21.0万
  • 财政年份:
    2007
  • 负责人:
    Dinakar Ramakrishnan
  • 依托单位:
Problems in Automorphic Forms, Arithmetic and Geometry
  • 批准号:
    0402044
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $21.0万
  • 财政年份:
    2004
  • 负责人:
    Dinakar Ramakrishnan
  • 依托单位:
Automorphic Forms, L-functions and Galois Representations
  • 批准号:
    0100372
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $16.97万
  • 财政年份:
    2001
  • 负责人:
    Dinakar Ramakrishnan
  • 依托单位:
国内基金
海外基金
Handbook of the Mathematics of the Arts and Sciences的中文翻译
  • 批准号:
    12226504
  • 项目类别:
    数学天元基金项目
  • 资助金额:
    20.0万元
  • 批准年份:
    2022
  • 负责人:
    黄朝凌
  • 依托单位:
SCIENCE CHINA: Earth Sciences
Journal of Environmental Sciences
SCIENCE CHINA Information Sciences