Computational number theory : proceedings of the Colloquium on Computational Number Theory held at Kossuth Lajos University, Debrecen (Hungary), September 4-9, 1989 / editors, Attila Pethö [and others]
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 ordersApplications 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 / ZassenhausHecke 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 algorithmOn Thue equations associated with certain quartic number fields; KANT -- a tool for computations in algebraic number fields; SIMATH -- a computer algebra system
Bibliography
Includes bibliographical references
Notes
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