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

• M. J. Bertin -- Mesure de Mahler et régulateur elliptique: Preuve de deux relations exotiques
• A. Besser -- The \(p\)-adic height pairings of Coleman-Gross and of Nekovář
• J. M. Borwein and K.-K. S. Choi -- Dirichlet series for squares of sums of squares: A summary
• D. Burns -- Equivariant Whitehead torsion and refined Euler characteristics
• A. C. Cojocaru -- Questions about the reductions modulo primes of an elliptic curve
• C. Consani and M. Marcolli -- New perspectives in Arakelov geometry
• H. Darmon -- A fourteenth lecture on Fermat's last theorem
• W. Duke -- Number fields with large class group
• S. J. Gurak -- Period polynomials for \(\mathbb{F}_q\) of fixed small degree
• J. Hanke -- Some recent results about (ternary) quadratic forms
• L. Jones -- An extension of a theorem of D. H. Lehmer
• S.-i. Katayama, C. Levesque, and T. Nakahara -- On a family of real bicyclic biquadratic fields
• C. Khare -- Belyi parametrisations of elliptic curves and congruence defects
• H. H. Kim -- An application of exterior square functoriality of \(GL_4\); Asai lift
• M. Laurent -- Totally real integral points on a plane algebraic curve
• L. Murata and C. Pomerance -- On the largest prime factor of a Mersenne number
• M. R. Murty and S. Sumner -- On the \(p\)-adic series \(\sum_{n=1}^{\infty} n^k\cdot n!\)
• K. Ono -- Hecke operators and the \(q\)-expansion of modular forms
• D. P. Roberts -- An ABC construction of number fields
• D. Roy -- Diophantine approximation in small degree
• L. Smithline -- Compact operators with rational generation
• V. Talamanca -- The canonical height of a finite étale \(K\)-algebra