THE 'LARGE SIEVE' METHOD AND ITS APPLICATIONS IN THE THEORY OF NUMBERS

Abstract

CONTENTS Notation Introduction § 1. The essence of the method. First applications § 2. The probabilistic interpretation of the 'large sieve' § 3. Composite moduli. Application to binary additive problems § 4. The non-vanishing of L-functions near the line § 5. A distribution theorem for the number of classes of primitive quadratic forms with negative determinant § 6. ΣR-equidistribution of prime numbers. Application to A. Selberg' s sieve § 7. The central limit theorem for additive arithmetic functions, given on the set of values of a polynomial for a ΣR-equidistributed sequence § 8. The order of the mean values of multiplicative functions on the set of values of a polynomial for a ΣR-equidistributed sequence References