The central topic of this research monograph is the relation
between p-adic modular forms and p-adic Galois representations, and
in particular the theory of deformations of Galois representations
recently introduced by Mazur. The classical theory of modular forms
is assumed known to the reader, but the p-adic theory is reviewed
in detail, with ample intuitive and heuristic discussion, so that
the book will serve as a convenient point of entry to research in
that area. The results on the U operator and on Galois
representations are new, and will be of interest even to the
experts. A list of further problems in the field is included to
guide the beginner in his research. The book will thus be of
interest to number theorists who wish to learn about p-adic modular
forms, leading them rapidly to interesting research, and also to
the specialists in the subject.
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