Number Theory

Abelian l-Adic Representations and Elliptic Curves..

This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable...

Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers—Ramanujan identities and will include related historical material that is unavailable elsewhere...

Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms...

Diophantine analysis is an extremely active field in number theory because of its many open problems and conjectures. Requiring only a basic understanding of number theory, Diophantine Analysis is built around the detailed theory of continued fractions and features many applications and examples. Th..

This book presents several basic techniques in algebraic geometry, group representations, number theory, l-adic and standard cohomology, and modular forms. It explores how NX(p) varies with p when the family (X) of polynomial equations is fixed. The text examines the size and congruence properties o..

Linear Algebra and Geometry..

Exploring fresh developments as well as fundamental concepts, Syzygies and Hilbert Functions presents highlights, conjectures, unsolved problems, and examples of Hilbert functions and resolutions. The book studies the role of these functions in the areas of algebraic geometry and combinatorics. It a..

The Mathematics of Ciphers..

Clearly written and well organized, this treatise presents material not found in other books on Lie groups. It systematically explores the structural aspects of complex Lie groups, beginning with general concepts then moving to the theory of representative functions of Lie groups and the extension p..

This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and re..