Mathematical Sciences: Metaplectric Eisenstein Series and Theta Functions

本研究的第一部分是关于一般线性群上的亚辛型理论中的一些问题。这些问题涉及到具有尖点形式的theta函数和其他theta函数的卷积，以及theta函数和抛物线Eisenstein级数的傅立叶系数的性质。本研究的第二部分是将这一工作推广到研究四维自旋群双覆盖上的亚普勒型，并讨论了它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.