Mathematical Sciences: L Functions With Applications to the Oscillator Representation

本研究涉及自同构表示的L-函数的构造及其在涉及振荡器表示的问题中的各种应用。我们将把西格尔-韦尔公式推广到一般情况。我们的目标是对任意自同构形式，尤其是爱森斯坦级数的对应有一个一般的描述。自同构l -函数是各种算术函数的生成函数，并在其解析性质中编码了大量信息。获得这些类型的函数如何表现的一般理论是本研究的中心焦点。

This research is concerned with the construction of L- functions of automorphic representations and of various applications to problems involving the oscillator representation. Work will be done to generalize the Siegel-Weil formula to the general case. The goal will be to have a general description of the theta correspondence of any automorphic form, especially Eisenstein series. Automorphic L-functions are generating functions of various arithmetic functions and manage to encode much information in their analytic properties. Obtaining general theories of how these types of functions behave is the central focus of this research.