**Fields Institute Communications**

Volume: 41;
2004;
392 pp;
Hardcover

MSC: Primary 11; 94; 14;

Print ISBN: 978-0-8218-3353-7

Product Code: FIC/41

List Price: $129.00

Individual Member Price: $103.20

**Electronic ISBN: 978-1-4704-3075-7
Product Code: FIC/41.E**

List Price: $129.00

Individual Member Price: $103.20

# High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams

Share this page *Edited by *
*Alf van der Poorten; Andreas Stein*

A co-publication of the AMS and Fields Institute

This volume consists of a selection of papers based on presentations made at the international conference on number theory held in honor of Hugh Williams' sixtieth birthday. The papers address topics in the areas of computational and explicit number theory and its applications. The material is suitable for graduate students and researchers interested in number theory.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Readership

Graduate students and research mathematicians interested in number theory.

# Table of Contents

## High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams

- Cover Cover11
- Title page iii4
- Contents v6
- Preface ix10
- The streets of Alberta xi12
- Hugh Cowie Williams xiii14
- Group photo xiv15
- Constructing elliptic curves with a known number of points over a prime field 116
- On a generalization of the radix representation–A survey 1934
- Multiplicative structure of values of the Euler function 2944
- Congruences and exponential sums with the Euler function 4964
- On the existence of cyclic difference sets with small parameters 6176
- Doubly focused enumeration of locally square polynomial values 6984
- Cubic reciprocity and explicit primality tests for ℎ⋅3^{𝑘}±1 7792
- Algorithms for finding almost irreducible and almost primitive trinomials 91106
- Commentary on Lucas’ test 103118
- Number field cryptography 111126
- Reconfigurable computing machines and their applications in computational number theory 123138
- Heuristics for class numbers of prime-power real cyclotomic fields 149164
- Counting 𝐴₄ and 𝑆₄ number fields with given resolvent cubic 159174
- On a conjecture of Feit and Thompson 169184
- Amicable pairs, a survey 179194
- On the research contributions of Hugh C. Williams 197212
- Hilbert modular fourfolds of arithmetic genus one 217232
- Values of ternary recurrence sequences and torsion on certain curves arising from the work of Hugh Williams 227242
- Divisibility of exponents of class groups of pure cubic number fields 237252
- New conjectures and results for small cycles of the discrete logarithm 245260
- Hyperelliptic curves and cryptography 255270
- Remarks on S. Chowla’s hypothesis implying that 𝐿(𝑠,𝜒)>0 for 𝑠>0 and for real characters 𝜒 283298
- On the computation of cube roots modulo 𝑝 293308
- Jeepers, creepers, … 305320
- Algebraic tori in cryptography 317332
- An analysis of the generalized binary GCD algorithm 327342
- An elliptic curve trapdoor system (extended abstract) 341356
- Periodic continued fractions and elliptic curves 353368
- The Cunningham project 367382
- Extensions and improvements for the CM method for genus two 379394
- Advice to referees of submissions to High Primes and Misdemeanours 391406
- Back Cover Back Cover1410