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.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1971
Accession Number
AD0734836

Entities

People

  • H. Halberstam

Organizations

  • University of Nottingham

Tags

Communities of Interest

  • Counter WMD

DTIC Thesaurus Topics

  • Additives (Chemicals)
  • Arithmetic
  • Difference Equations
  • Equations
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • Number Theory
  • Numbers
  • Numerical Integration
  • Polynomials
  • Prime Numbers
  • Sequences
  • Sequences (Mathematics)
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Military History of the United States in the 20th Century.
  • Systems Analysis and Design