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 -- Primeproducing 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