Cuprins
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
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