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High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams
 
Edited by: Alf van der Poorten Centre for Number Theory Research, Killara, NSW, Australia
Andreas Stein University of Illinois at Urbana-Champaign, Urbana, IL
A co-publication of the AMS and Fields Institute
High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams
Hardcover ISBN:  978-0-8218-3353-7
Product Code:  FIC/41
List Price: $144.00
MAA Member Price: $129.60
AMS Member Price: $115.20
eBook ISBN:  978-1-4704-3075-7
Product Code:  FIC/41.E
List Price: $136.00
MAA Member Price: $122.40
AMS Member Price: $108.80
Hardcover ISBN:  978-0-8218-3353-7
eBook: ISBN:  978-1-4704-3075-7
Product Code:  FIC/41.B
List Price: $280.00 $212.00
MAA Member Price: $252.00 $190.80
AMS Member Price: $224.00 $169.60
High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams
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High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams
Edited by: Alf van der Poorten Centre for Number Theory Research, Killara, NSW, Australia
Andreas Stein University of Illinois at Urbana-Champaign, Urbana, IL
A co-publication of the AMS and Fields Institute
Hardcover ISBN:  978-0-8218-3353-7
Product Code:  FIC/41
List Price: $144.00
MAA Member Price: $129.60
AMS Member Price: $115.20
eBook ISBN:  978-1-4704-3075-7
Product Code:  FIC/41.E
List Price: $136.00
MAA Member Price: $122.40
AMS Member Price: $108.80
Hardcover ISBN:  978-0-8218-3353-7
eBook ISBN:  978-1-4704-3075-7
Product Code:  FIC/41.B
List Price: $280.00 $212.00
MAA Member Price: $252.00 $190.80
AMS Member Price: $224.00 $169.60
  • Book Details
     
     
    Fields Institute Communications
    Volume: 412004; 392 pp
    MSC: 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 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
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 412004; 392 pp
MSC: 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 co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

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 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.