Introduction to Shimura Varieties
by J.S. Milne
Number of pages: 149
This is an introduction to the theory of Shimura varieties, or, in other words, to the arithmetic theory of automorphic functions and holomorphic automorphic forms. Because of their brevity, many proofs have been omitted or only sketched.
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by Pete L. Clark - University of Georgia
The goal is to find and explore open questions in both geometry of numbers -- e.g. Lattice Point Enumerators, the Ehrhart-Polynomial, Minkowski's Convex Body Theorems, Minkowski-Hlawka Theorem, ... -- and its applications to number theory.
by Edward Nelson - Princeton Univ Pr
The book based on lecture notes of a course given at Princeton University in 1980. From the contents: the impredicativity of induction, the axioms of arithmetic, order, induction by relativization, the bounded least number principle, and more.
by Greg W. Anderson - The University of Arizona
This is a compilation of exercises, worked examples and key references that the author compiled in order to help readers learn their way around fermionic Fock space. The text is suitable for use by graduate students with an interest in number theory.
by J.S. Milne - BookSurge Publishing
This book, intended for research mathematicians, proves the duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry, for example, in the proof of Fermat's Last Theorem.