AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

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

About this Title

Alf van der Poorten, Centre for Number Theory Research, Killara, NSW, Australia and Andreas Stein, University of Illinois at Urbana-Champaign, Urbana, IL, Editors

Publication: Fields Institute Communications
Publication Year: 2004; Volume 41
ISBNs: 978-0-8218-3353-7 (print); 978-1-4704-3075-7 (online)
DOI: https://doi.org/10.1090/fic/041
MathSciNet review: MR2070919
MSC: Primary 11-06; Secondary 00B30

View full volume as PDF

Read more about this volume

Table of Contents

Download chapters as PDF

Front/Back Matter

• View this volume's front and back matter

Chapters

• Amod Agashe, Kristin Lauter and Ramarathnam Venkatesan – Constructing elliptic curves with a known number of points over a prime field
• S. Akiyama, T. Borbély, H. Brunotte, A. Pethő and J. Thuswaldner – On a generalization of the radix representation–A survey
• William Banks, John Friedlander, Carl Pomerance and Igor Shparlinski – Multiplicative structure of values of the Euler function
• William Banks and Igor Shparlinski – Congruences and exponential sums with the Euler function
• Leonard Baumert and Daniel Gordon – On the existence of cyclic difference sets with small parameters
• Daniel Bernstein – Doubly focused enumeration of locally square polynomial values
• Wieb Bosma – Cubic reciprocity and explicit primality tests for $h\cdot 3^k\pm 1$
• Richard Brent and Paul Zimmermann – Algorithms for finding almost irreducible and almost primitive trinomials
• John Brillhart – Commentary on Lucas’ test
• Johannes Buchmann, Tsuyoshi Takagi and Ulrich Vollmer – Number field cryptography
• Duncan Buell, S. Devarkal and Heather Wake – Reconfigurable computing machines and their applications in computational number theory
• Joe Buhler, Carl Pomerance and Leanne Robertson – Heuristics for class numbers of prime-power real cyclotomic fields
• Henri Cohen – Counting $A_4$ and $S_4$ number fields with given resolvent cubic
• Karl Dilcher and Joshua Knauer – On a conjecture of Feit and Thompson
• Mariano García, Jan Pedersen and Herman te Riele – Amicable pairs, a survey
• Andrew Granville – On the research contributions of Hugh C. Williams
• H. Grundman and L. Lippincott – Hilbert modular fourfolds of arithmetic genus one
• E. Herrmann and P. Walsh – Values of ternary recurrence sequences and torsion on certain curves arising from the work of Hugh Williams
• Santos Hernández and Florian Luca – Divisibility of exponents of class groups of pure cubic number fields
• Joshua Holden and Pieter Moree – New conjectures and results for small cycles of the discrete logarithm
• Michael Jacobson, Jr., Alfred Menezes and Andreas Stein – Hyperelliptic curves and cryptography
• Stéphane Louboutin – Remarks on S. Chowla’s hypothesis implying that $L(s,\chi )>0$ for $s>0$ and for real characters $\chi$
• Siguna Müller – On the computation of cube roots modulo $p$
• Roger Patterson and Alfred van der Poorten – Jeepers, creepers, $\ldots$
• Karl Rubin and Alice Silverberg – Algebraic tori in cryptography
• Jonathan Sorenson – An analysis of the generalized binary GCD algorithm
• Edlyn Teske – An elliptic curve trapdoor system (extended abstract)
• Alfred van der Poorten – Periodic continued fractions and elliptic curves
• Samuel Wagstaff, Jr. – The Cunningham project
• Annegret Weng – Extensions and improvements for the CM method for genus two
• Alfred van der Poorten and Andreas Stein – Advice to referees of submissions to High Primes and Misdemeanours