**CRM Proceedings & Lecture Notes**

Volume: 19;
1999;
392 pp;
Softcover

MSC: Primary 11;

Print ISBN: 978-0-8218-0964-8

Product Code: CRMP/19

List Price: $128.00

AMS Member Price: $102.40

MAA Member Price: $115.20

**Electronic ISBN: 978-1-4704-3933-0
Product Code: CRMP/19.E**

List Price: $128.00

AMS Member Price: $102.40

MAA Member Price: $115.20

# Number Theory: Fifth Conference of the Canadian Number Theory Association

Share this page *Edited by *
*Rajiv Gupta; Kenneth S. Williams*

A co-publication of the AMS and Centre de Recherches Mathématiques

This book contains papers presented at the fifth Canadian Number Theory Association (CNTA) conference held at Carleton University (Ottawa, ON). The invited speakers focused on arithmetic algebraic geometry and elliptic curves, diophantine problems, analytic number theory, and algebraic and computational number theory. The contributed talks represented a wide variety of areas in number theory. David Boyd gave an hour-long talk on “Mahler's Measure and Elliptic Curves”. This lecture was open to the public and attracted a large audience from outside the conference.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Readership

Graduate students and research mathematicians working in number theory and related fields.

# Table of Contents

## Number Theory: Fifth Conference of the Canadian Number Theory Association

- Cover Cover11
- Title page v6
- Dedication vii8
- Pál Erdős, 26 March, 1913–20 September, 1996 ix10
- Contents xi12
- Preface xv16
- Conference banquet in honour of Richard K. Guy xvii18
- List of lectures xxi22
- List of registrants xxix30
- Rational curves with zero self intersection on certain 𝐾3 surfaces 134
- Notes on Ramanujan’s singular moduli 740
- The operator 𝑥+(1/𝑥)-2 and the reciprocal integers 1750
- Integral points on cubic surfaces 2558
- The last exhaustive computation of class groups of complex quadratic number fields 3568
- Diophantine approximation in projective space 5588
- Bounds for odd perfect numbers 67100
- Automorphic 𝐿-functions in level aspect 73106
- The number field sieve on many computers 81114
- On the order of 𝑎 (mod 𝑝) 87120
- A special case of Cohen-Lenstra heuristics in function fields 99132
- An asymptotic expansion of Ramanujan 107140
- Improving Ramachandra’s and Levesque’s unit index 111144
- On the middle factor of the period polynomial for finite fields 121154
- On the distribution of champs 133166
- Sextic number fields with discriminant (-1)^{𝑗}2^{𝑎}3^{𝑏} 141174
- Traces of singular moduli and the Fourier coefficients of the elliptic modular function 𝑗(𝜏) 173206
- Problème d’Eisenstein pour le conducteur 3 177210
- Liens entre le théorème de Mason et la conjecture (𝑎𝑏𝑐) 187220
- On the trace of Hecke operators for Maass forms 215248
- An analysis of Shanks’s algorithm for computing square roots in finite fields 231264
- On the equation 𝑎₁𝑝₁+𝑎₂𝑝₂+𝑎₃𝑝₃=𝑏 with prime variables in arithmetic progressions 243276
- Solutions to 𝑥²-𝐷𝑦²=𝑄 265298
- Integers represented by ternary quadratic forms 281314
- Some uniformity results following from the Lang conjectures 291324
- Fourier coefficients of cusp forms 297330
- Beer and continued fractions with periodic periods 309342
- An inequality for polynomials 315348
- Some integrals of theta functions in Ramanujan’s lost notebook 323356
- Arithmetic of a certain Calabi-Yau threefold 333366
- Diophantine approximation in Euclidean spaces 341374
- Transcendance et indépendance algébrique de valeurs de fonctions modulaires 353386
- On the rank of ideal class groups 377410
- Conference problems session conducted by J. L. Selfridge 385418
- Homework! 391424
- Back Cover Back Cover1426