Automorphic forms, L-functions and the relative trace formula

自守形式、L-函数和相对迹公式

• 批准号: 1201446
• 负责人: Brooke Feigon
• 金额: $ 16.97万
• 依托单位: CUNY City College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-05-01 至 2016-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1201446&HistoricalAwards=false
• 关键词: Automorphic; forms; functions; relative; trace

The relative trace formula is an important tool in the study of automorphic forms and the Langlands program. Jacquet invented the relative trace formula to study period integrals of automorphic forms, in particular, to establish criteria for certain cases of functoriality in terms of non-vanishing of periods. More recently, work has been done in some cases relating the value of the period explicitly to special values of L-functions. The importance of the relative trace formula is widely recognized and the field is far from exhausted. The PI plans on generalizing to higher rank groups a result of Waldspurger and Jacquet linking L-values with period integrals, extending work of hers on a subconvex bound and generalizing results of hers on an average L-value formula to higher degree L-functions where much less is known. In addition, she will continue her work in computing statistics for curves over finite fields by looking at the distribution of the zeros of the zeta functions of a family of Artin-Schreier curves defined over a finite field as the genus of the family increases.The PI's proposal includes a plan to mentor and conduct research with undergraduate students at The City College of New York. This institution has a diverse student body consisting of large numbers of traditionally underrepresented groups, in terms of race, ethnicity and socio-economic background. In addition the PI will continue her work mentoring women in mathematics.

相对痕量公式是自动形式研究和兰兰兹计划研究中的重要工具。雅克（Jacquet）发明了针对自动形式的研究期积分的相对痕量公式，尤其是在不进行时期的范围内建立某些功能性案例的标准。最近，在某些情况下，已经完成了将周期的价值明确与L功能的特殊值有关的工作。相对痕迹公式的重要性被广泛认可，并且该场远非疲惫。 PI计划概括更高排名小组，这是Waldspurger和Jacquet将L值与周期积分联系起来的结果少得多。此外，她将通过查看一个在有限领域定义的Zeta函数的Zeta功能的分布来继续在有限领域的计算曲线计算统计数据方面的统计数据。 PI的建议包括一项计划，与纽约市城市学院的本科生指导和进行研究。在种族，种族和社会经济背景方面，该机构具有多样化的学生团体，包括大量传统代表性的群体。此外，PI将继续她的工作指导数学女性。