eBook ISBN:  9781470430757 
Product Code:  FIC/41.E 
List Price:  $136.00 
MAA Member Price:  $122.40 
AMS Member Price:  $108.80 
eBook ISBN:  9781470430757 
Product Code:  FIC/41.E 
List Price:  $136.00 
MAA Member Price:  $122.40 
AMS Member Price:  $108.80 

Book DetailsFields Institute CommunicationsVolume: 41; 2004; 392 ppMSC: Primary 11; 94; 14
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 copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipGraduate students and research mathematicians interested in number theory.

Table of Contents

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 primepower 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


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
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 copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students and research mathematicians interested in number theory.

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 primepower 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