On the prime ideal theorem and irregularities in the
              distribution of primes

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On the prime ideal theorem and irregularities in the distribution of primes

M. Nair and A. Perelli

Source: Duke Math. J. Volume 77, Number 1 (1995), 1-20.

First Page PDF: View first page of article (PDF, 64 KB)

Primary Subjects: 11N05

Secondary Subjects: 11N32

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077286144
Mathematical Reviews number (MathSciNet): MR1317625
Zentralblatt MATH identifier: 0818.11035
Digital Object Identifier: doi:10.1215/S0012-7094-95-07701-1

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References

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[2] R. Brauer, On the zeta-functions of algebraic number fields, Amer. J. Math. 69 (1947), 243–250.

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[3] H. Davenport, Multiplicative Number Theory, 2nd ed., Graduate Texts in Mathematics, vol. 74, Springer-Verlag, Berlin, 1980.

Mathematical Reviews (MathSciNet): MR82m:10001

Zentralblatt MATH: 0453.10002

[4] J. Friedlander and A. Granville, Limitations to the equi-distribution of primes I, Ann. of Math. (2) 129 (1989), no. 2, 363–382.

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Zentralblatt MATH: 0671.10041

Digital Object Identifier: doi:10.2307/1971450

JSTOR: links.jstor.org

[5] J. Friedlander and A. Granville, Limitations to the equi-distribution of primes IV, Proc. Roy. Soc. London Ser. A 435 (1991), no. 1893, 197–204.

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Zentralblatt MATH: 0736.11049

[6] P. X. Gallagher, A large sieve density estimate near $\sigma =1$, Invent. Math. 11 (1970), 329–339.

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Digital Object Identifier: doi:10.1007/BF01403187

[7] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, New York, 1974.

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Zentralblatt MATH: 0298.10026

[8] G. H. Hardy and J. E. Littlewood, Some problems of partitio numerorum. III. On the expression of a number as a sum of primes, Acta Math. 44 (1923), 1–70.

Zentralblatt MATH: 48.0143.04

Digital Object Identifier: doi:10.1007/BF02403921

[9] H. Heilbronn, On real zeros of Dedekind $\zeta$-functions, Canad. J. Math. 25 (1973), 870–873.

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[10] H. Maier, Primes in short intervals, Michigan Math. J. 32 (1985), no. 2, 221–225.

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Digital Object Identifier: doi:10.1307/mmj/1029003189

Project Euclid: euclid.mmj/1029003189

[11] M. Nair and A. Perelli, Sieve methods and class-number problems I, J. Reine Angew. Math. 367 (1986), 11–26.

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[12] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts in Mathematics, vol. 80, Cambridge University Press, Cambridge, 1981.

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Zentralblatt MATH: 0455.10034

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On the prime ideal theorem and irregularities in the distribution of primes

References

Duke Mathematical Journal