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Abstract: Let Q(x; y) be a primitive positive de nite quadratic form with integer coecients. Then, for all (s; t) 2 R 2 there exist (m; n) 2 Z 2 such that Q(m;n) is prime and Q(m s; n t) Q(s; t) 0:53 : This is deduced from another result giving an estimate for the number of prime ideals in an ideal class of an imaginary quadratic number field that fall in a given sector and whose norm lies in a short interval. (Update)
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BibTeX entry: (Update)
@misc{ harman-distribution,
author = "G. Harman and A. Kumchev and P. A. Lewis",
title = "The Distribution Of Prime Ideals Of Imaginary Quadratic Fields",
url = "citeseer.ist.psu.edu/485084.html" }
Citations (may not include all citations):69 The Theory of the Riemann Zeta-Function (context) - Titchmarsh - 1986
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22 Elementary and Analytic Theory of Algebraic Numbers (context) - Narkiewicz - 1974
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9 erence between consecutive primes (context) - Huxley, di - 1972
6 erence between consecutive primes (context) - Heath-Brown, Iwaniec et al. - 1979
3 The number of primes in a short interval (context) - Heath-Brown - 1988
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2 The distribution of points at which binary quadratic forms a.. (context) - Coleman - 1990
1 The exceptional set for Goldbach's problem in short interval.. (context) - Baker, Harman et al. - 1997
1 with an application (context) - sieve, elds - 1993
1 of theorem and some applications (context) - Rademacher, PhragmenLindel - 1959
1 Gaussian primes in narrow sectors (context) - Harman, Lewis
Documents on the same site (http://www.math.toronto.edu/kumchev/):
Diophantine Approximation By Cubes Of Primes And An Almost.. - Brüdern, Kumchev (2001) (Correct)
On A Binary Diophantine Inequality Involving Prime Powers - Kumchev, Laporta (Correct)
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