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

• A. Baragar -- Rational curves with zero self intersection on certain $K$3 surfaces
• B. C. Berndt and H. H. Chan -- Notes on Ramanujan's singular moduli
• M.-J. Bertin -- The operator $x +(1/x)-2$ and the reciprocal integers
• F. Beukers -- Integral points on cubic surfaces
• D. A. Buell -- The last exhaustive computation of class groups of complex quadratic number fields
• K.-K. Choi and J. D. Vaaler -- Diophantine approximation in projective space
• R. J. Cook -- Bounds for odd perfect numbers
• W. Duke -- Automorphic $L$-functions in level aspect
• R.-M. Elkenbracht-Huizing, P. L. Montgomery, R. D. Silverman, R. K. Wackerbarth, and S. S. Wagstaff, Jr. -- The number field sieve on many computers
• P. Erdős and M. R. Murty -- On the order of $a$ (mod $p$)
• C. Friesen -- A special case of Cohen-Lenstra heuristics in function fields
• W. F. Galway -- An asymptotic expansion of Ramanujan
• C. Greither -- Improving Ramachandra's and Levesque's unit index
• S. Gurak -- On the middle factor of the period polynomial for finite fields
• A. Ivić and C. Pomerance -- On the distribution of champs
• J. W. Jones and D. P. Roberts -- Sextic number fields with discriminant $(-1)^j2^a3^b$
• M. Kaneko -- Traces of singular moduli and the Fourier coefficients of the elliptic modular function $j(\tau)$
• P. Kaplan -- Problème d'Eisenstein pour le conducteur 3
• M. Langevin -- Liens entre le théorème de Mason et la conjecture $(abc)$
• X.-J. Li -- On the trace of Hecke operators for Maass forms
• S. Lindhurst -- An analysis of Shanks's algorithm for computing square roots in finite fields
• M.-C. Liu and T. Wang -- On the equation $a_1p_1 + a_2p_2 + a_3p_3 = b$ with prime variables in arithmetic progressions
• S. Louboutin and R. A. Mollin -- Solutions to $x^2 - Dy^2 = Q$
• K. Ono and K. Soundararajan -- Integers represented by ternary quadratic forms
• P. L. Pacelli -- Some uniformity results following from the Lang conjectures
• Y. N. Petridis -- Fourier coefficients of cusp forms
• A. J. van der Poorten -- Beer and continued fractions with periodic periods
• C. J. Smyth -- An inequality for polynomials
• S. H. Son -- Some integrals of theta functions in Ramanujan's lost notebook
• H. A. Verrill -- Arithmetic of a certain Calabi-Yau threefold
• L. Ya. Vulakh -- Diophantine approximation in Euclidean spaces
• M. Waldschmidt -- Transcendance et indépendance algébrique de valeurs de fonctions modulaires
• S. Wong -- On the rank of ideal class groups
• R. K. Guy -- Conference problems session conducted by J. L. Selfridge
• P. Ribenboim -- Homework!