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Lectures on Siegel modular forms and representation by quadratic forms. (English) Zbl 0596.10020

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 J. S. Hsia, the author and 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.
Reviewer: M.Peters

MSC:

11E12 Quadratic forms over global rings and fields
11-02 Research exposition (monographs, survey articles) pertaining to number theory
11F27 Theta series; Weil representation; theta correspondences
11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)

Citations:

Zbl 0374.10013