Classical Theory of Algebraic Numbers

Gauss created the theory of binary quadratic forms in tDisquisitiones Arithmeticaev and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem. These were the s tarting points for the theory of algebraic numbers, developed in the c lassical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many o thers. This theory, enriched with more recent contributions, is of bas ic importance in the study of diophantine equations and arithmetic alg ebraic geometry, including methods in cryptography.