الصفحة 1
الصفحة 1
Undergraduate Algebra
Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text.
The Heat Kernel and Theta Inversion on SL2(C)
The present monograph develops the fundamental ideas and results surrounding heat kernels, spectral theory, and regularized traces associated to the full modular group acting on SL2(C). The authors begin with the realization of the heat kernel on SL2(C) through spherical transform, from which one manifestation of the heat kernel on quotient spaces is obtained through group periodization. From a different point of view, one constructs the heat kernel on the group space using an eigenfunction, or spectral, expansion, which then leads to a theta function and a theta inversion formula by equating the two realizations of the heat kernel on the quotient space. The trace of the heat kernel diverges, which naturally leads to a regularization of the trace by studying Eisenstein series on the eigenfunction side and the cuspidal elements on the group periodization side.
Posn(R) and Eisenstein Series
Posn(R) and Eisenstein Series provides an introduction, requiring minimal prerequisites, to the analysis on symmetric spaces of positive definite real matrices as well as quotients of this space by the unimodular group of integral matrices. The approach is presented in very classical terms and includes material on special functions, notably gamma and Bessel functions, and focuses on certain mathematical aspects of Eisenstein series.
