Cohomology of arithmetic groups serves as a tool in studying possible relations between the theory of automorphic forms and the arithmetic of algebraic varieties resp.
Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level.
It was the aim of the Erlangen meeting in May 1988 to bring together number theoretists and algebraic geometers to discuss problems of common interest, such as moduli problems, complex tori, integral points, rationality questions, automorphic forms.
The New York Number Theory Seminar was organized in 1982 to provide a forum for the presentation and discussion of recent advances in higher arithmetic and its applications.
This book is a general introduction to Higher AlgebraicK-groups of rings and algebraic varieties, which were firstdefined by Quillen at the beginning of the 70's.
These are notes of lectures on Nevanlinna theory, in the classical case of meromorphic functions, and the generalization by Carlson-Griffith to equidimensional holomorphic maps using as domain space finite coverings of C resp.
"e;This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations.
The 15 papers of this selection of contributions to the Journees Arithmetiques 1987 include both survey articles and original research papers and represent a cross-section of topics such as Abelian varieties, algebraic integers, arithmetic algebraic geometry, additive number theory, computational number theory, exponential sums, modular forms, transcendence and Diophantine approximation, uniform distribution.
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.
An international Summer School on: "e;Modular functions of one variable and arithmetical applications"e; took place at RUCA, Antwerp University, from July 17 to - gust 3, 1972.
Cyclotomic fields have always occupied a central place in number theory, and the so called "e;main conjecture"e; on cyclotomic fields is arguably the deepest and most beautiful theorem known about them.
One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory.
For the most part, this book is the translation from Japanese of the earlier book written jointly by Koji Doi and the author who revised it substantially for the English edition.
Eugene Charles Catalan made his famous conjecture - that 8 and 9 are the only two consecutive perfect powers of natural numbers - in 1844 in a letter to the editor of Crelle's mathematical journal.
