Devoted to the interaction of modern scientific computation and classical number theory, covering subjects from effective finiteness results to efficient algorithms in elementary, analytical and algebraic number theory, these papers provide a broad review of methods and results in the area.

I-IV -- Preface -- List of contributors -- Table of contents -- On the construction of primitive elements and primitive normal bases in a finite field -- A numerical method for the determination of the cyclotomic polynomial coefficients -- Number systems -- Fast converging series representations of real numbers and their implementations in digital processing -- On a polynomial transformation and its application to the construction of a public key cryptosystem -- Number-theoretic transforms and a theorem of Sylvester - Kronecker - Zsigmondy -- A probabilistic class group and regulator algorithm and its implementation -- Prime-producing quadratic polynomials and class numbers of quadratic orders -- Applications of a new class number two criterion for real quadratic fields -- On a solution of a class number two problem for a family of real quadratic fields -- Cubic number fields with exceptional units -- Enumeration of totally complex quartic fields of small discriminant -- Class number computation by cyclotomic or elliptic units -- Computing fundamental units from independent units -- A note on index divisors -- Computation of independent units in number fields by a combination of the methods of Buchmann/Pethö and Pohst / Zassenhaus -- Hecke actions on classes of ternary quadratic forms -- Computation of singular moduli by multi-valued modular equations -- Congruent numbers and elliptic curves -- The rank of elliptic curves upon quadratic extension -- On the resolution of some diophantine equations -- Index form equations in cubic number fields -- On the practical solution of the Thue-Mahler equation -- Some results on Thue equations and Thue-Mahler equations -- On the solution of the diophantine equation Gn = P(x) with sieve algorithm -- On Thue equations associated with certain quartic number fields -- KANT - a tool for computations in algebraic number fields -- SIMATH - a computer algebra system