"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions.
This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a...
"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of vario...
From the reviews: ..". The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail....
From the reviews: ..". The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a w...
Starting with the end of the seventeenth century, one of the most interesting directions in mathematics (attracting the attention as J. Bernoulli, Euler, Jacobi, Legendre, Abel, among others) has been the study of integrals of the form r dz l Aw(T) = -, TO W where w is an algebraic function of z. Such integrals are now called abelian. Let us examine the simplest instance of an abelian integral, one where w is defined by the polynomial equation (1) where the polynomial on the right hand side has no multiple roots. In this case the function Aw is called an elliptic integral. The value of Aw is...
Starting with the end of the seventeenth century, one of the most interesting directions in mathematics (attracting the attention as J. Bernoulli, Eul...
The problems being solved by invariant theory are far-reaching generalizations and extensions of problems on the "reduction to canonical form" of various is almost the same thing, projective geometry. objects of linear algebra or, what Invariant theory has a ISO-year history, which has seen alternating periods of growth and stagnation, and changes in the formulation of problems, methods of solution, and fields of application. In the last two decades invariant theory has experienced a period of growth, stimulated by a previous development of the theory of algebraic groups and commutative...
The problems being solved by invariant theory are far-reaching generalizations and extensions of problems on the "reduction to canonical form" of vari...
This EMS volume provides an exposition of the structure theory of Fano varieties, i.e. algebraic varieties with an ample anticanonical divisor. This book will be very useful as a reference and research guide for researchers and graduate students in algebraic geometry.
This EMS volume provides an exposition of the structure theory of Fano varieties, i.e. algebraic varieties with an ample anticanonical divisor. Thi...
This book was written over a period of more than six years. Several months after we finished our work, N.1. Fel'dman (the senior author of the book) died. All additions and corrections entered after his death were made by his coauthor. The assistance of many of our colleagues was invaluable during the writing of the book. They examined parts of the manuscript and suggested many improvements, made useful comments and corrected many errors. I much have pleasure in acknowledging our great indebtedness to them. Special thanks are due to A. B. Shidlovskii, V. G. Chirskii, A.1. Galochkin and O. N....
This book was written over a period of more than six years. Several months after we finished our work, N.1. Fel'dman (the senior author of the book) d...
