INTRODUCTION THE BASIC THEORY Weierstrass Equations The Group Law Projective Space and the Point at Infinity Proof of Associativity Other Equations for Elliptic Curves Other Coordinate Systems The… Expand

In these lectures, we give a very utilitarian description of the Galois cohomology needed in Wiles’ proof. For a more general approach, see any of the references. First we fix some notation. For a… Expand

Using the "simplest cubic fields" of D. Shanks, we give a modified proof and an extension of a result of Uchida, showing how to obtain cyclic cubic fields with class number divisible by n, for any n.… Expand

Abstract We give an explicit p -adic expansion of ∑ np j =1, ( j , p )=1 j − r as a power series in n . The coefficients are values of p -adic L -functions.