Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of A. O. L. Atkin

Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of A. O. L. Atkin

by Duncan A. Buell, J. T. Teitelbaum, A. O. Atkin
     
 

ISBN-10: 082180880X

ISBN-13: 9780821808801

Pub. Date: 12/02/1997

Publisher: American Mathematical Society

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

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Overview

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.

Product Details

ISBN-13:
9780821808801
Publisher:
American Mathematical Society
Publication date:
12/02/1997
Series:
AMS/IP Studies in Advanced Mathematics Series, #7
Pages:
232
Product dimensions:
7.09(w) x 9.84(h) x (d)

Table of Contents

Intelligent primality test offer1
Atkin and the Atlas lab13
Elliptic and modular curves over finite fields and related computational issues21
Algorithms for computing isogenies between elliptic curves77
Supersingular j-invariants hypergeometric series, and Atkin's orthogonal polynomials97
On the density of modular representations127
Numerical experiments on families of p-adic modular forms143
Ramanujan graphs159
Elliptic curves, Kloosterman sums, and Ramanujan graphs179
Binary cubic forms and cubic number fields191
Rigorous discrete logarithm computations in finite fields via smooth polynomials221

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