Lectures on Siegel modular forms and representation by quadratic forms (Q1078229)

The book considers the problem which quadratic forms are represented by a given quadratic form and how often. One approach is arithmetical: this is handled in Chapter 2, which gives a self-contained proof of the results of a paper by \textit{J. S. Hsia}, the author and \textit{M. Kneser} [J. Reine Angew. Math. 301, 132-141 (1978; Zbl 0374.10013)]. The other approach is analytic, considering theta series and Eisenstein series and estimating Fourier coefficients: this is done in Chapter 1, which gives a self- contained description of methods developed in recent papers by the author. The book is written clearly and gives a good introduction up to the frontiers of research in this area.