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Bombieri's theorem in short intervals

Published online by Cambridge University Press:  26 February 2010

M. N. Huxley  and
H. Iwaniec
M. N. Huxley
Affiliation:
Department of Pure Mathematics, University College, Cardif
H. Iwaniec
Affiliation:
Mathematics Institute, Polish Academy of Sciences, Warsaw, Poland
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Extract

Let x, y, Q denote large real numbers, with x > y > Q. The object of this paper is to prove the following result

for arbitrary A > 0, with a larger value of Q than hitherto. The symbol denotes as usual the suppression of an absolute constant, π(N; q, a) denotes the number of prime numbers up to N which are congruent to a (mod q), and ϕ(q) denotes Euler's function.

Type
Research Article
Information
Mathematika , Volume 22 , Issue 2 , December 1975 , pp. 188 - 194
Copyright
Copyright © University College London 1975

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