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

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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.