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Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of A. O. L. Atkin
Edited by: D. A. Buell, Center for Computing Sciences, Bowie, MD, and J. T. Teitelbaum, University of Illinois at Chicago, IL
A co-publication of the AMS and International Press of Boston, Inc..

AMS/IP Studies in Advanced Mathematics
1998; 232 pp; softcover
Volume: 7
ISBN-10: 0-8218-0880-X
ISBN-13: 978-0-8218-0880-1
List Price: US$75
Member Price: US$60
Order Code: AMSIP/7
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This volume contains papers presented at the conference, "Computational Perspectives on Number Theory" held at the University of Illinois at Chicago in honor of the retirement of A. O. L. Atkin. In keeping with Atkin's interests and work, the papers cover a range of topics, including algebraic number theory, \(p\)-adic modular forms, and modular curves. Many of the papers reflect Atkin's particular interest in computational and algorithmic questions.

Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.


Graduate students and research mathematicians working in computational number theory.

Table of Contents

  • A. O. L. Atkin -- Intelligent primality test offer
  • B. Birch -- Atkin and the Atlas Lab
  • N. D. Elkies -- Elliptic and modular curves over finite fields and related computational issues
  • R. Lercier and F. Morain -- Algorithms for computing isogenies between elliptic curves
  • M. Kaneko and D. Zagier -- Supersingular \(j\)-invariants, hypergeometric series, and Atkin's orthogonal polynomials
  • F. Gouvea and B. Mazur -- On the density of modular representations
  • R. Coleman, G. Stevens, and J. Teitelbaum -- Numerical experiments on families of \(p\)-adic modular forms
  • A. Pizer -- Ramanujan graphs
  • W. Li -- Elliptic curves, Kloosterman sums, and Ramanujan graphs
  • K. Belabas and H. Cohen -- Binary cubic forms and cubic number fields
  • R. L. Bender and C. Pomerance -- Rigorous discrete logarithm computations in finite fields via smooth polynomials
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