Abelian varieties are special examples of projective varieties. As such theycan be described by a set of homogeneous polynomial equations. The theory ofabelian

Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, w

Based on the work in algebraic geometry by Norwegian mathematician Niels Henrik Abel (1802–29), this monograph was originally published in 1959 and reprinted

From Gauss to G|del, mathematicians have sought an efficient algorithm to distinguish prime numbers from composite numbers. This book presents a random polynomi

Presents a modern treatment of the theory of theta functions in the context of algebraic geometry.