Attila Pethoe & Michael Pohst 
Computational Number Theory [PDF ebook] 
Proceedings of the Colloquium on Computational Number Theory held at Kossuth Lajos University, Debrecen (Hungary), September 4-9, 1989

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