Cover

Title page

Dedication

Pál Erdős, 26 March, 1913–20 September, 1996

Contents

Preface

Conference banquet in honour of Richard K. Guy

List of lectures

List of registrants

Rational curves with zero self intersection on certain 𝐾3 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)^{𝑗}2^{𝑎}3^{𝑏}

Traces of singular moduli and the Fourier coefficients of the elliptic modular function 𝑗(𝜏)

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 𝑎₁𝑝₁+𝑎₂𝑝₂+𝑎₃𝑝₃=𝑏 with prime variables in arithmetic progressions

Solutions to 𝑥²-𝐷𝑦²=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!

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