A note on index divisors

Chapters in this book

1. I-IV I
2. Preface V
3. List of contributors VII
4. Table of contents XI
5. On the construction of primitive elements and primitive normal bases in a finite field 1
6. A numerical method for the determination of the cyclotomic polynomial coefficients 15
7. Number systems 21
8. Fast converging series representations of real numbers and their implementations in digital processing 27
9. On a polynomial transformation and its application to the construction of a public key cryptosystem 31
10. Number-theoretic transforms and a theorem of Sylvester - Kronecker - Zsigmondy 45
11. A probabilistic class group and regulator algorithm and its implementation 53
12. Prime—producing quadratic polynomials and class numbers of quadratic orders 73
13. Applications of a new class number two criterion for real quadratic fields 83
14. On a solution of a class number two problem for a family of real quadratic fields 95
15. Cubic number fields with exceptional units 103
16. Enumeration of totally complex quartic fields of small discriminant 129
17. Class number computation by cyclotomic or elliptic units 139
18. Computing fundamental units from independent units 163
19. A note on index divisors 173
20. Computation of independent units in number fields by a combination of the methods of Buchmann/Pethö and Pohst / Zassenhaus 183
21. Hecke actions on classes of ternary quadratic forms 191
22. Computation of singular moduli by multi-valued modular equations 213
23. Congruent numbers and elliptic curves 227
24. The rank of elliptic curves upon quadratic extension 239
25. On the resolution of some diophantine equations 261
26. Index form equations in cubic number fields 281
27. On the practical solution of the Thue-Mahler equation 289
28. Some results on Thue equations and Thue-Mahler equations 295
29. On the solution of the diophantine equation Gn = P(x) with sieve algorithm 303
30. On Thue equations associated with certain quartic number fields 313
31. KANT - a tool for computations in algebraic number fields 321
32. SIMATH - a computer algebra system 331