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Number Theory: Fifth Conference of the Canadian Number Theory Association

Edited by: Rajiv Gupta University of British Columbia, Vancouver, BC, Canada
Kenneth S. Williams Carleton University, Ottawa, ON, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques
Available Formats:
Softcover ISBN: 978-0-8218-0964-8
Product Code: CRMP/19
List Price: $128.00 MAA Member Price:$115.20
AMS Member Price: $102.40 Electronic ISBN: 978-1-4704-3933-0 Product Code: CRMP/19.E List Price:$128.00
MAA Member Price: $115.20 AMS Member Price:$102.40
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $192.00 MAA Member Price:$172.80
AMS Member Price: $153.60 Click above image for expanded view Number Theory: Fifth Conference of the Canadian Number Theory Association Edited by: Rajiv Gupta University of British Columbia, Vancouver, BC, Canada Kenneth S. Williams Carleton University, Ottawa, ON, Canada A co-publication of the AMS and Centre de Recherches Mathématiques Available Formats:  Softcover ISBN: 978-0-8218-0964-8 Product Code: CRMP/19  List Price:$128.00 MAA Member Price: $115.20 AMS Member Price:$102.40
 Electronic ISBN: 978-1-4704-3933-0 Product Code: CRMP/19.E
 List Price: $128.00 MAA Member Price:$115.20 AMS Member Price: $102.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$192.00 MAA Member Price: $172.80 AMS Member Price:$153.60
• Book Details

CRM Proceedings & Lecture Notes
Volume: 191999; 392 pp
MSC: Primary 11;

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.

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

• Chapters
• Rational curves with zero self intersection on certain $K$3 surfaces
• Notes on Ramanujan’s singular moduli
• The operator $x +(1/x)-2$ and the reciprocal integers
• Integral points on cubic surfaces
• The last exhaustive computation of class groups of complex quadratic number fields
• Diophantine approximation in projective space
• Bounds for odd perfect numbers
• Automorphic $L$-functions in level aspect
• The number field sieve on many computers
• On the order of $a$ (mod $p$)
• A special case of Cohen-Lenstra heuristics in function fields
• An asymptotic expansion of Ramanujan
• Improving Ramachandra’s and Levesque’s unit index
• On the middle factor of the period polynomial for finite fields
• On the distribution of champs
• Sextic number fields with discriminant $(-1)^j2^a3^b$
• Traces of singular moduli and the Fourier coefficients of the elliptic modular function $j(\tau )$
• Problème d’Eisenstein pour le conducteur 3
• Liens entre le théorème de Mason et la conjecture $(abc)$
• On the trace of Hecke operators for Maass forms
• An analysis of Shanks’s algorithm for computing square roots in finite fields
• On the equation $a_1p_1 + a_2p_2 + a_3p_3 = b$ with prime variables in arithmetic progressions
• Solutions to $x^2 - Dy^2 = Q$
• Integers represented by ternary quadratic forms
• Some uniformity results following from the Lang conjectures
• Fourier coefficients of cusp forms
• Beer and continued fractions with periodic periods
• An inequality for polynomials
• Some integrals of theta functions in Ramanujan’s lost notebook
• Arithmetic of a certain Calabi-Yau threefold
• Diophantine approximation in Euclidean spaces
• Transcendance et indépendance algébrique de valeurs de fonctions modulaires
• On the rank of ideal class groups
• Conference problems session conducted by J. L. Selfridge
• Homework!
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 191999; 392 pp
MSC: Primary 11;

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.

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

• Chapters
• Rational curves with zero self intersection on certain $K$3 surfaces
• Notes on Ramanujan’s singular moduli
• The operator $x +(1/x)-2$ and the reciprocal integers
• Integral points on cubic surfaces
• The last exhaustive computation of class groups of complex quadratic number fields
• Diophantine approximation in projective space
• Bounds for odd perfect numbers
• Automorphic $L$-functions in level aspect
• The number field sieve on many computers
• On the order of $a$ (mod $p$)
• A special case of Cohen-Lenstra heuristics in function fields
• An asymptotic expansion of Ramanujan
• Improving Ramachandra’s and Levesque’s unit index
• On the middle factor of the period polynomial for finite fields
• On the distribution of champs
• Sextic number fields with discriminant $(-1)^j2^a3^b$
• Traces of singular moduli and the Fourier coefficients of the elliptic modular function $j(\tau )$
• Problème d’Eisenstein pour le conducteur 3
• Liens entre le théorème de Mason et la conjecture $(abc)$
• On the trace of Hecke operators for Maass forms
• An analysis of Shanks’s algorithm for computing square roots in finite fields
• On the equation $a_1p_1 + a_2p_2 + a_3p_3 = b$ with prime variables in arithmetic progressions
• Solutions to $x^2 - Dy^2 = Q$
• Integers represented by ternary quadratic forms
• Some uniformity results following from the Lang conjectures
• Fourier coefficients of cusp forms
• Beer and continued fractions with periodic periods
• An inequality for polynomials
• Some integrals of theta functions in Ramanujan’s lost notebook
• Arithmetic of a certain Calabi-Yau threefold
• Diophantine approximation in Euclidean spaces
• Transcendance et indépendance algébrique de valeurs de fonctions modulaires
• On the rank of ideal class groups
• Conference problems session conducted by J. L. Selfridge
• Homework!
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.