**CRM Proceedings & Lecture Notes**

Volume: 36;
2004;
303 pp;
Softcover

MSC: Primary 11;

Print ISBN: 978-0-8218-3331-5

Product Code: CRMP/36

List Price: $109.00

AMS Member Price: $87.20

MAA member Price: $98.10

**Electronic ISBN: 978-1-4704-3950-7
Product Code: CRMP/36.E**

List Price: $109.00

AMS Member Price: $87.20

MAA member Price: $98.10

# Number Theory

Share this page *Edited by *
*Hershy Kisilevsky; Eyal Z. Goren*

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

This volume contains a collection of articles from the meeting of the Canadian Number Theory Association held at the Centre de Recherches Mathématiques (CRM) at the University of Montreal. The book represents a cross section of current research and new results in number theory. Topics covered include algebraic number theory, analytic number theory, arithmetic algebraic geometry, computational number theory, and Diophantine analysis and approximation. The volume contains both research and expository papers suitable for graduate students and researchers interested in number theory.

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

#### Readership

Graduate students and research mathematicians interested in number theory.

# Table of Contents

## Number Theory

- Cover Cover11
- Title page iii4
- Contents v6
- List of participants vii8
- List of speakers xvii18
- Preface xxiii24
- Mesure de Mahler et régulateur elliptique: Preuve de deux relations exotiques 126
- The 𝑝-adic height pairings of Coleman-Gross and of Nekovář 1338
- Dirichlet series for squares of sums of squares: A summary 2752
- Equivariant Whitehead torsion and refined Euler characteristics 3560
- Questions about the reductions modulo primes of an elliptic curve 6186
- New perspectives in Arakelov geometry 81106
- A fourteenth lecture on Fermat’s last theorem 103128
- Number fields with large class group 117142
- Period polynomials for 𝔽_{𝕢} of fixed small degree 127152
- Some recent results about (ternary) quadratic forms 147172
- An extension of a theorem of D. H. Lehmer 165190
- On a family of real bicyclic biquadratic fields 177202
- Belyi parametrisations of elliptic curves and congruence defects 189214
- An application of exterior square functoriality of 𝐺𝐿₄; Asai lift 197222
- Totally real integral points on a plane algebraic curve 203228
- On the largest prime factor of a Mersenne number 209234
- On the 𝑝-adic series ∑_{𝑛=1}^{∞}𝑛^{𝑘}⋅𝑛! 219244
- Hecke operators and the 𝑞-expansion of modular forms 229254
- An ABC construction of number fields 237262
- Diophantine approximation in small degree 269294
- Compact operators with rational generation 287312
- The canonical height of a finite étale 𝐾-algebra 295320
- Back Cover Back Cover1329