Mathematical Sciences: Metaplectric Eisenstein Series and Theta Functions

本研究的第一部分是关于一般线性群的形而上学形式理论中的一些问题。这些问题与带尖角形式的函数和其他函数的卷积有关，与函数的傅里叶系数的性质以及抛物线爱森斯坦级数有关。本研究的第二部分是将本工作推广到四维自旋群双盖上的元塑形式的研究，以及在数论中的一些应用。

The first part of this research is concerned with some problems in the theory of metaplectic forms on the general linear group. These problems are related to convolutions of theta functions with cusp forms and with other theta functions and to the nature of the Fourier coefficients of theta functions and parabolic Eisenstein series. The second part of this research is concerned with an extension of this work to the study of metaplectic forms on the double cover of the four dimensional spin group and with some applications to number theory.