A broad introduction to quadratic forms, modular functions, interpretation by rings and ideals, class fields by radicals and more. 1985 ed.

In this graduate level textbook, Professor Cohn takes a problem that Pythagoras could have posed, and using it as motivation, develops a constructional introduction to classical field theory and modular function theory. The interest in constructional techniques has increased recently with the advent of cheap and plentiful computer technology. The beginning chapters provide the motivation and necessary background in elementary algebraic number theory and Riemann surface theory. The ideas and results are then applied and extended to class field theory. In the later chapters, more specialized results are presented, with full proofs, though the author emphasizes, with examples, the relation of the material to other parts of mathematics.

Papers about algebraic geometry and their applications.

Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.

Stark's conjectures on the behavior of USDLUSD-functions were formulated in the 1970s. Since then, these conjectures and their generalizations have been actively investigated. This has led to significant progress in algebraic number theory. The current volume, based on the conference held at Johns Hopkins University (Baltimore, MD), represents the state-of-the-art research in this area. The first four survey papers provide an introduction to a majority of the recent work related to themes currently under exploration in the area, such as non-abelian and USDpUSD-adic aspects of the conjectures, abelian refinements, etc. Among others, some important contributors to the volume include Harold M. Stark, John Tate, and interested in number theory.

New York Number Theory Seminar started its regular meeting in January, 1982. The Seminar has been meeting on a regular basis weekly during the academic year since then. The meeting place of the seminar is in midtown Manhattan at the Graduate School and University Center of the City Uni versity of New York. This central location allows number-theorists in the New York metropolitan area and vistors an easy access. Four volumes of the Seminar proceedings, containing expanded texts of Seminar's lectures had been published in the Springer's Lecture Notes in Mathematics series as volumes 1052 (1984), 1135 (1985), 1240 (1987), and 1383 (1989). Seminar co chairmen are pleased that some of the contributions to the Seminar opened new avenues of research in Number Theory and related areas. On a histori cal note, one of such contributions proved to be a contribution by P. Landweber. In addition to classical and modern Number Theory, this Semi nar encourages Computational Number Theory. This book presents a selection of invited lectures presented at the New York Number Theory Seminar during 1989-1990. These papers cover wide areas of Number Theory, particularly modular functions, Aigebraic and Diophantine Geometry, and Computational Number Theory. The review of C-L. Chai presents a broad view of the moduli of Abelian varieties based on recent work of the author and many other prominent experts. This provides the reader interested in Diophantine Analysis with access to state of the art research. The paper of D. V. and G. V.

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Euler-Lagrange mapping - Helmholtz form and the inverse problem - Symmetries and the Noether’s theory of conservation laws - Regularity and the Hamilton theory - Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces

This book details the classical part of the theory of algebraic number theory, excluding class-field theory and its consequences. Coverage includes: ideal theory in rings of algebraic integers, p-adic fields and their finite extensions, ideles and adeles, zeta-functions, distribution of prime ideals, Abelian fields, the class-number of quadratic fields, and factorization problems. The book also features exercises and a list of open problems.