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The distribution of polynomial sequences

Published online by Cambridge University Press:  26 February 2010

H. Halberstam  and
H.-E. Richert
H. Halberstam
Affiliation:
Mathematics Department, University of Nottingham.
H.-E. Richert
Affiliation:
Abteilung för Mathematik, Universität Ulm, Germany.
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Extract

Prime number theory is concerned with the distribution of primes in sequences of natural numbers, such as arithmetic progressions or polynomial sequences. An extensive range of such questions is embraced by

Hypothesis H (Schinzel, see [10]. Let f1, …, fgbe distinct irreducible polynomials in Z[x] (with positive leading coefficients) and suppose that f1 …fghas no fixed prime divisors. Then there exist infinitely many integers n such that each fi (n) (i = 1, …, g) is prime.

Type
Research Article
Information
Mathematika , Volume 19 , Issue 1 , June 1972 , pp. 25 - 50
Copyright
Copyright © University College London 1972

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References

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