Bessel Models and the Transfer of Siegel Cusp Forms of Degree 2

贝塞尔模型和 2 次西格尔尖端形式的传递

• 批准号: 1100541
• 负责人: Ameya Pitale
• 金额: $ 28.51万
• 依托单位: University of Oklahoma Norman Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-10-01 至 2015-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1100541&HistoricalAwards=false
• 关键词: Bessel; Models; Transfer; Siegel; Cusp

A proposal is made for a detailed study of Bessel models for the group GSp(4) over a nonarchimedean local field, and the application of the results to analytic properties of L-functions, the non-generic transfer of Siegel modular forms to GL(4), and special values of L-functions. The importance of Whittaker models in the theory of Automorphic Representations is well known. For certain groups such as GSp(4) Bessel models can serve as a substitute for those representations that have no Whittaker model. While general facts for Bessel models are known, such as the uniqueness of Bessel models, certain important questions remain unanswered and prevent a widespread deployment of these models. Amongst the unknown facts are the determination of test vectors for a given representation and a given Bessel model, and the calculation of explicit Bessel functions. This research will close these knowledge gaps, allowing for several new applications of Bessel models.The activity of this proposal will promote teaching, training, and learning via the inclusion of graduate students as participants in the proposed research. The activity of this proposal will broaden the participation of under-represented groups. The PI and the Co-PI plan to continue their close contacts with the OU McNair Scholars Programs well as the Sooner Traditions Scholars program of the University of Oklahoma. These programs are comprised of undergraduate students which are either first-generation and low-income, or from underrepresented groups, or from traditionally disadvantaged high-schools in the Oklahoma City and Tulsa area. The activity of this proposal will enhance infrastructure for research and education. As part of the Automorphic Forms group at the University of Oklahoma, the PI and the Co-PI have participated, and will continue to participate, in a number of scientific activities involving researchers and students from other institutions. Amongst these activities are joint seminars with neighboring universities and conferences with a largely regional appeal. Other activities will include short- and medium-term visits from researchers from other parts of the country and also from overseas. Finally, the activity of the proposed research will lead, within the framework of the Automorphic Forms group of the University of Oklahoma, to the creation of a website with resources for students and researchers in the area of Automorphic Forms. Amongst other things, the web site will contain a comprehensive list of activities in Automorphic Forms.

本文提出了一个关于非阿基米德局部域上群GSp（4）的Bessel模型的详细研究的建议，并将研究结果应用于L-函数的解析性质、Siegel模形式到GL（4）的非一般转移以及L-函数的特殊值。Whittaker模型在自守表示理论中的重要性是众所周知的。对于某些群体，如GSp（4），贝塞尔模型可以作为没有惠特克模型的那些表示的替代品。虽然贝塞尔模型的一般事实是已知的，如贝塞尔模型的独特性，某些重要的问题仍然没有答案，并阻止这些模型的广泛部署。在未知的事实是一个给定的表示和一个给定的贝塞尔模型的测试向量的确定，并计算显式贝塞尔函数。这项研究将缩小这些知识差距，允许贝塞尔模型的几个新的应用程序。这项建议的活动将促进教学，培训和学习，通过纳入研究生作为参与者在拟议的研究。这项建议的活动将扩大代表性不足群体的参与。PI和Co-PI计划继续与俄克拉荷马州大学的McNair学者计划和Sooner Scholars Scholars计划保持密切联系。这些项目由本科生组成，他们要么是第一代低收入者，要么来自代表性不足的群体，要么来自俄克拉荷马州市和塔尔萨地区传统上处于不利地位的高中。这项建议的活动将加强研究和教育的基础设施。作为俄克拉荷马州大学自守形式小组的一部分，PI和Co-PI已经参加并将继续参加一些涉及其他机构研究人员和学生的科学活动。在这些活动中，有与邻近大学的联合研讨会和具有很大区域吸引力的会议。其他活动将包括来自该国其他地区和海外的研究人员的短期和中期访问。最后，拟议的研究活动将导致，在俄克拉荷马州大学自守形式组的框架内，创建一个网站，为自守形式领域的学生和研究人员提供资源。除其他事项外，该网站将载有一份以自守形式开展的活动的综合清单。