Montgomery's weighted sieve for dimension two |
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Authors: | Dr H Siebert |
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Institution: | (1) Abteilung für Mathematik III, Universität Ulm (MNH), Oberer Eselsberg, D-7900 Ulm, Federal Republic of Germany |
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Abstract: | The most well-known application of Montgomery's weighted sieve is to the so-called Brun-Titchmarsh inequality, which was proved byH. L. Montgomery andR. C. Vaughan in the form (x, k, l)2x((k)log(x/k))–1 for 1k<x, (k, l)=1, (x, k, l) being the number of primespx andpl modk, (k) being Euler's function. In this paper an upper estimate is given for a certain class of two-dimensional sieve problems, among them bounds for the number of twin primes and the number of Goldbach representations. |
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