Advances in Number Theory: The Proceedings of the Third Conference of the Canadian Number Theory Association

The key feature at this conference was the 33 invited papers from the world's leading number theorists. Talks were in three sessions: analytical number theory; arithmetical algebraic geometry; and diophantive approximation. Speakers included: F.Beukers (University of Utrecht); R. Heath-Brown (Oxford); H.L. Montgomery (Ann Arbor, Michigan); T. Nakahara (Saga University, Japan); Y. Zarhin (Academy of Science, USSR).

Table of Contents:
Preface List of Invited Addresses List of Contributed Talks Conference Participants Picture List of Contributors 1: Plenary Addresses 1.1: F. Beukers: Exotic values of G-functions 1.2: John B. Friedlander: Irregularities in the Distribution of Primes 1.3: D.R. Heath-Brown: The Dirichlet Divisor Problem 1.4: M. Ram Murty: A Motivated Introduction to the Langlands Program 1.5: Michael Waldschmidt: Transcendental Numbers and Functions of Several Variables 1.6: F. Rodriguez Villegas and Don Zagier: Square roots of central values of Hecke L-series 2: Analytic Number Theory Invited Addresses 2.1: Henryk Iwaniec: A Formula for the Fourier Coefficients of Maass Cusp Forms 2.2: M. Jutila: The Additive Divisor Problem and Exponential Sums 2.3: Hugh L. Montgomery: Distribution of Small Powers of a Primitive Root Contributed Talks 2.4: A. Knopfmacher, J. Knopfmacher and R. Warlimont: Ordered Factorizations for Integers and Arithmetical Semigroups 2.5: Toru Nakahara: A Simple Proof for Non-Monogenesis of the Rings of Integers in some Cyclic Fields 2.6: Jukka Pihko: Representing integers as sums of squares and Hypothesis H 3: Arithmetical Algebraic Geometry Invited Addresses 3.1: Hendrik W. Lenstra, Jr. and Yuri G. Zarhin: The Tate Conjecture for Almost Ordinary Abelian Varieties over Finite Fields 3.2: V. Kumar Murty: The Notion of a Shimura Variety 3.3: Takayuki Oda: Galois Action on the Nilpotent Completion of the Fundamental Group of an Algebraic Curve 3.4: Paul Vojta: Arithmetic of Subvarieties of Abelian and Semiabelian Varieties Contributed Talks 3.5: Harvey Cohn: Projection from an Algebraic Quadratic Form to Rational Quadratic Forms 3.6: Teresa Crespo: Construction of S4-fields and modular forms of weight 1 3.7: Paul Feit: A Universal Format for Local/Global Theories 3.8: Alan J. Laing: Shimura Reciprocity for Modular Functions with Rational Fourier Coefficients 3.9: Joan-C. Lario: On Serre's conjecture (3.2.4?) and vertical Weil Curves 3.10: Odile Lecacheux: Units in Number Fields and Elliptic Curves 3.11: Jaap Top: Descent by 3-isogeny and 3-Rank of quadratic fields 3.12: Yuri Tschinkel: Finite heights and rational points on surfaces Chapter IV: Diophantine Approximation Invited Addresses 4.1: David W. Boyd: Linear recurrence for some generalized Pisot sequences 4.2: W. Dale Brownawell: Algebraic Independence of Drinfeld Exponential and Quasi-Periodic Functions 4.3: Jan-Hendrik Evertse: Estimates for Discriminate and Resultants of Binary Forms 4.4: Julia Mueller: A note on Thue's inequality with few coefficients Contributed Talks 4.5: M.J. Bertin: K-Nombres de Pisot et de Salem 4.6: J. Brüdern and R.J. Cook: Cubic Inequalities of Additive Type 4.7: Henri Faure: Discrepance et Diaphone en Dimension Un 4.8: Noriko Hirata-Kohno: Une Relation Entre les Points Entiers sur une Courbe Algébrique et les Points Rationels de la Jacobienne 4.9: Micehl Langevin: Problèmes de Favard et de Lehmer Generalisés 4.10: Damien Roy: On the v-adic independence of algebraic numbers 4.11: A.J. van der Poorten: Continued fractions of formal power series Chapter V: Session in Honour of Paulo Ribenboim Plenary Address 5.1: Andrew Granville: Paulo Ribenboim, at the time of his retirement 5.2: Andrew Granville: The Kummer-Wieferich-Skula Approach to the First Case of Fermat's Last Theorem Invited Addresses 5.3: S. Louboutin, R.A. Mollin, and H.C. Williams: Class Groups of exponent two in real quadratic fields 5.4: J. Miná^c: Poincaré Polynomials, Stability Indices and Number of Orderings I 5.5: Speeches at the Banquet in Honour of P. Ribenboim 5.6: T.M. Viswanathan: Paulo Ribenboim: three aspects of his career Paulo Ribenboim: Response

Review :
'The size of this volume is a testimony to the variety and interest of the material presented at the conference.' L'Enseignement Mathématique, 3-4 1993