Theory of Numbers
Abstract
The first part of the paper deals with a class of divisor problems. The average of the divisor function (the number of representations as a product of k factors) over numbers of the form p-a, p < or = x (p prime) is tied up with a certain conjecture about the distribution of primes in arithmetic progressions. The second part describes numerical work by J. W. Porter in connection with Selberg's sieve which, when joined with some recent theorems of Halberstam and Richert, yields new results in additive prime number theory. The third part is a survey by H. Halberstam of recent progress, largely due to Richert and himself, towards the notorious Hypothesis H of Schinzel concerning prime values assumed simultaneously by numbers of integer valued polynomials.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1971
- Accession Number
- AD0734836
Entities
People
- H. Halberstam
Organizations
- University of Nottingham