Théorie des nombres / Number Theory: Proceedings of the International Number Theory Conference held at Université Laval, July 5-18, 1987

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Théorie des nombres / Number Theory

Proceedings of the International Number Theory Conference held at Université Laval, July 5-18, 1987

Edited by: Jean M. de Koninck and Claude Levesque

Language: French

Published/Copyright: 1989

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De Gruyter Proceedings in Mathematics

Topics

Mathematics Algebra and Number Theory

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I-IV
I

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Introduction
V

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Remerciements / Acknowledgements
IX

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Liste des participants / List of participants
XI

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Table des matières / Table of contents
XVII

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Exponential Diophantine equations
1
L. J. Alex and L. L. Foster

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Quantitative aspects of the representations of integers by quadratic forms
7
A. Arenas

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Diagonal cubic equations, I
15
R.C. Baker

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Irrational dilations of approximate multiplicative semigroups of integers
29
Daniel Berend

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Some special features of the Jacobi group
41
Rolf Berndt

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Généralisation de suites de Pisot et de suites de Boyd
51
Μ. J . Bertin

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Salem numbers of degree four have periodic expansions
57
David W. Boyd

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Applications of partition theory to groups: Covering the alternating group by products of conjugacy classes
65
J . L . Brenner and R . J . List

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Variation of local heights on an algebraic family of abelian varieties
72
Gregory S. Call

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Sur une fausse forme modulaire liée à des identités de Ramanujan et Andrews
97
Henri Cohen

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Global orders in definite quaternion algebras as endomorphism rings for reduced CM elliptic curves
108
David R. Dorman

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Distribution properties of continuous curves
117
Michael Drmota and Robert F. Tichy

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On the torsion in quotients of the multiplicative groups in abelian extensions
128
D. S. Dummit

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Binary quadratic forms over rings of algebraic integers: a survey of recent results
133
A.G. Earnest

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Places totalement décomposées dans des Zp-extensions d'un corps de nombres
160
Michel Emsalem

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Grandes valeurs de fonctions liées aux diviseurs premiers consécutifs d'un entier
169
Paul Erdös and Jean-Louis Nicolas

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The maximal order and the average order of multiplicative function σ(e)(n)
201
J. Fabrykowski and M.V. Subbarao

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Discrépance quadratique de suites infinies en dimension un
207
Henri Faure

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Integral solutions of linear systems
213
Mary E. Flahive

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Fractional parts of sequences
220
John B. Friedlander

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On the distribution of divisor class groups of curves over a finite field
227
Eduardo Friedman and Lawrence C. Washington

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Diophantine approximation, Kronecker's limit formula and the Riemann Hypothesis
240
Akio Fujii

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Le théorème de Riemann-Roch et les corps de nombres algébriques
251
Paul Gérardin

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Functional equations and periodic sequences
267
Paul Gérardin and Wen-Ch'ing Winnie Li

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Zp-extensions of function fields
280
R. Gold and H. Kisilevsky

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Pseudoprimes on elliptic curves
290
Daniel M. Gordon

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Least primes in arithmetic progressions
306
Andrew Granville

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Cyclic Galois extensions and normal bases
322
Cornelius Greither

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Cubic and biquadratic pseudoprimes of Lucas type
330
S. Gurak

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On some mean value results for the Riemann zeta-function
348
J.L. Hafner and A. Ivić

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Classical explicit reciprocity
359
Charles Hélou

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The distribution of badly approximable numbers and continuants with bounded digits
371
Doug Hensley

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Approximation de périodes de fonctions méromorphes
386
Noriko Hirata

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L-series of automorphic forms on GL(3,R)
398
Jeff Hoffstein and M. Ram Murty

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Equations differentielles Fuchsiennes et approximations diophantiennes
409
Marc Huttner

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Exponential sums and the Riemann zeta function
417
M.N. Huxley

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Some recent results on the Riemann zeta-function
424
Aleksandar Ivić

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On the representations of a group as a Galois group over an arbitrary field
441
C. U. Jensen

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On evaluation of certain limits in closed form
459
S. Kanemitsu

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Potential theory on curves
475
Ernst Kani

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Characterization of arithmetical functions, problems and results
544
I. Kátai

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On a sufficient condition for the p—class tower of a CM—field to be infinite
556
H. Kisilevsky and J. Labute

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Calculation of general Gauss sums and quadratic Gauss sums in finite rings
561
E. Lamprecht

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Transfinite diameter and Favard's problems on diameters of algebraic integers
574
M. Langevin, E. Reyssat and G. Rhin

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Poles of Dirichlet series and D-modules
579
Ben Lichtin

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Small prime solutions of linear equations
595
Ming-Chit Liu and Kai-Man Tsang

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Unusually large gaps between consecutive primes
625
Helmut Maier and Carl Pomerance

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On the congruence for Gauss sums and its applications
633
Hiroo Miki

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On central extensions
642
Katsuya Miyake

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Prime producing quadratic polynomials and real quadratic fields of class number one
654
R.A. Mollin and H.C. Williams

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Disjoint systems of rational Beatty sequences
664
R. Morikawa

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Complete determination of all torsion groups of elliptic curves with integral absolute invariant over quadratic and pure cubic fields
671
Hans H. Müller, Harald Stroher and Horst G. Zimmer

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On generalized zeta—functions
699
Helmut Müller

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Bounds for solutions of simultaneous diagonal equations of odd degree
703
T. Nadesalingam and Jane Pitman

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Long arithmetic progressions and powers of 2
735
Melvyn B. Nathanson

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Sur la cohomologie de certains modules galoisiens p-ramifiés
740
Thong Nguyen Quang Do

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On Euler's φ — function in quadratic number fields
755
Werner Georg Nowak

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Ternary code construction of even unimodular lattices
772
Michio Ozeki

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On the distribution of values of an error term related to the Euler function
785
Y.-F. S. Petermann

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Formes lineaires de logarithmes elliptiques et mesures de transcendance
798
Patrice Philippon and Michel Waldschmidt

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On a question of Tverberg
806
Jukka Pihko

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Titchmarsh series
811
Κ. Ramachandra

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Galois representations associated to generic formal groups
815
Michael Rosen and Karl Zimmermann

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A local construction of the local root numbers
823
Victor Snaith

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On Fermat d-pseudoprimes
841
Lawrence Somer

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Exponential sums of digit counting functions
861
Alan H. Stein

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Some computational results on a problem of Einsenstein
869
A.J. Stephens and H.C. Williams

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The Eisenstein measure and real quadratic fields
887
Glenn Stevens

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Carmichael's conjecture and some analogues
928
M.V. Subbarao and L.W. Yip

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The algebraic independence of three numbers: Schneider's method
942
Robert Tubbs

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The number of solutions of certain equations of the form f(xm) = g(yn) over a finite field
968
Robert G. Van Meter

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On entire functions assuming integer values in a geometric sequence
981
R. V. Wallisser

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Stickelberger's theorem for cyclotomic fields, in the spirit of Kummer and Thaine
990
Lawrence C. Washington

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A propos d'un lemme de Κ. Kato sur le groupe de Brauer en caractéristique ρ
994
Thomas Wyler

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1003-1006
1003

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Publishing information

Pages and Images/Illustrations in book

eBook published on:

June 15, 2011

eBook ISBN:

9783110852790

Hardcover published on:

September 1, 1989

Hardcover ISBN:

9783110117912

Edition:

Reprint 2011

Pages and Images/Illustrations in book

Front matter:

22

Main content:

1002

https://doi.org/10.1515/9783110852790

eBook ISBN: 9783110852790

Hardcover ISBN: 9783110117912

Keywords for this book

Zahlentheorie; Kongress; Quebec

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Théorie des nombres / Number Theory

Overview

Topics

Table of contents

I-IV

Introduction

Remerciements / Acknowledgements

Liste des participants / List of participants

Table des matières / Table of contents

Exponential Diophantine equations

Quantitative aspects of the representations of integers by quadratic forms

Diagonal cubic equations, I

Irrational dilations of approximate multiplicative semigroups of integers

Some special features of the Jacobi group

Généralisation de suites de Pisot et de suites de Boyd

Salem numbers of degree four have periodic expansions

Applications of partition theory to groups: Covering the alternating group by products of conjugacy classes

Variation of local heights on an algebraic family of abelian varieties

Sur une fausse forme modulaire liée à des identités de Ramanujan et Andrews

Global orders in definite quaternion algebras as endomorphism rings for reduced CM elliptic curves

Distribution properties of continuous curves

On the torsion in quotients of the multiplicative groups in abelian extensions

Binary quadratic forms over rings of algebraic integers: a survey of recent results

Places totalement décomposées dans des Zp-extensions d'un corps de nombres

Grandes valeurs de fonctions liées aux diviseurs premiers consécutifs d'un entier

The maximal order and the average order of multiplicative function σ(e)(n)

Discrépance quadratique de suites infinies en dimension un

Integral solutions of linear systems

Fractional parts of sequences

On the distribution of divisor class groups of curves over a finite field

Diophantine approximation, Kronecker's limit formula and the Riemann Hypothesis

Le théorème de Riemann-Roch et les corps de nombres algébriques

Functional equations and periodic sequences

Zp-extensions of function fields

Pseudoprimes on elliptic curves

Least primes in arithmetic progressions

Cyclic Galois extensions and normal bases

Cubic and biquadratic pseudoprimes of Lucas type

On some mean value results for the Riemann zeta-function

Classical explicit reciprocity

The distribution of badly approximable numbers and continuants with bounded digits

Approximation de périodes de fonctions méromorphes

L-series of automorphic forms on GL(3,R)

Equations differentielles Fuchsiennes et approximations diophantiennes

Exponential sums and the Riemann zeta function

Some recent results on the Riemann zeta-function

On the representations of a group as a Galois group over an arbitrary field

On evaluation of certain limits in closed form

Potential theory on curves

Characterization of arithmetical functions, problems and results

On a sufficient condition for the p—class tower of a CM—field to be infinite

Calculation of general Gauss sums and quadratic Gauss sums in finite rings

Transfinite diameter and Favard's problems on diameters of algebraic integers

Poles of Dirichlet series and D-modules

Small prime solutions of linear equations

Unusually large gaps between consecutive primes

On the congruence for Gauss sums and its applications

On central extensions

Prime producing quadratic polynomials and real quadratic fields of class number one

Disjoint systems of rational Beatty sequences

Complete determination of all torsion groups of elliptic curves with integral absolute invariant over quadratic and pure cubic fields

On generalized zeta—functions

Bounds for solutions of simultaneous diagonal equations of odd degree

Long arithmetic progressions and powers of 2

Sur la cohomologie de certains modules galoisiens p-ramifiés

On Euler's φ — function in quadratic number fields

Ternary code construction of even unimodular lattices

On the distribution of values of an error term related to the Euler function

Formes lineaires de logarithmes elliptiques et mesures de transcendance

On a question of Tverberg

Titchmarsh series

Galois representations associated to generic formal groups

A local construction of the local root numbers

On Fermat d-pseudoprimes

Exponential sums of digit counting functions

Some computational results on a problem of Einsenstein

The Eisenstein measure and real quadratic fields

Carmichael's conjecture and some analogues

The algebraic independence of three numbers: Schneider's method

The number of solutions of certain equations of the form f(xm) = g(yn) over a finite field