The second edition builds on the first in several ways. There are three new chapters which
survey recent directions and extensions of the theory, and there are two new appendices …

ItisnowwellknownthatFermat'slasttheoremhasbeenproved. For more than three and a half
centuries, mathematicians—from the greatnamestothecleveramateurs—triedtoproveFermat' …

Taniyama first suggested in the 1950's that a statement along these lines might be true, and
a precise conjecture was formulated by Shimura. A paper of Weil [Wei67] provided strong …

In the following paper we want to relate conjectures about solutions of the AB= C in global
fields with conjectures about elliptic curves. To do this we use the simple idea to interprete A …

This volume contains expanded versions of lectures given at an instructional conference on
number theory and arithmetic geometry held August 9 through 18, 1995 at Boston …

This textbook covers the basic properties of elliptic curves and modular forms, with emphasis
on certain connections with number theory. The ancient" congruent number problem" is the …

Recently, simply connected, three dimensional, projective varieties with trivial canonical
bundle have attracted the interest of physicists working on superstririg theory and algebraic …

One of the most intriguing problems of modern number theory is to relate the arithmetic of
abelian varieties to the special values of associated L-functions. A very precise conjecture …

This work is the product of my attempts to understand the list of possible singular fibres
which can occur on a rational elliptic surface with section, which has recently been produced …

This book uses the beautiful theory of elliptic curves to introduce the reader to some of the
deeper aspects of number theory. It assumes only a knowledge of the basic algebra …