Inventiones mathematicae

, Volume 11, Issue 4, pp 329–339 | Cite as

A large sieve density estimate near σ=1

  • P. X. Gallagher


Density Estimate Large Sieve Sieve Density 
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  1. 1.
    Bombieri, E.: On the large sieve. Mathematika12, 201–225 (1965).Google Scholar
  2. 2.
    —, Davenport, H.: On the large sieve method. Abhandlungen aus Zahlentheorie und Analysis. Berlin: VEB Deutscher Verlag der Wissenschaften 1968.Google Scholar
  3. 3.
    Chen, Jing-Run.: On the least prime in an arithmetical progression. Sci. Sinica14, 1868–1871 (1965).Google Scholar
  4. 4.
    Davenport, H.: Multiplicative number theory. Chicago: Markham 1967.Google Scholar
  5. 5.
    Fogels, E.: On the zeros ofL-functions. Acta Arith.11, 67–96 (1965).Google Scholar
  6. 6.
    Gallagher, P. X.: The large sieve. Mathematika14, 14–20 (1967).Google Scholar
  7. 7.
    Jutila, M.: A statistical density theorem forL-functions with applications. Acta Arith.16, 207–216 (1969).Google Scholar
  8. 8.
    —: On two theorems of Linnik concerning the zeros of Dirichlet'sL-functions. Ann. Acad. Sci. Fennicae.458, 1–32 (1969).Google Scholar
  9. 9.
    Knapowski, S.: On Linnik's theorem concerning exceptionalL-zeros. Publ. Math. Debrecen9, 168–178 (1962).Google Scholar
  10. 10.
    Linnik, Yu. V.: On the least prime in an arithmetic progression. Math. Sbornik., N.S.15 (57), 139–178, 347–367 (1944).Google Scholar
  11. 11.
    van Lint, J. H., Richert, H.-E.: On primes in arithmetic progressions. Acta Arith.11, 209–216 (1965).Google Scholar
  12. 12.
    Montgomery, H. L.: Mean and large values of Dirichlet polynomials. Inventiones math.8, 334–345 (1969).Google Scholar
  13. 13.
    —: Zeros ofL-functions. Invent. Math.8, 346–354 (1969).Google Scholar
  14. 14.
    Prachar, K.: Primzahlverteilung. Berlin-Göttingen-Heidelberg: Springer 1957.Google Scholar
  15. 15.
    Sos, V., Turán, P.: On some new theorems in the theory of diophantine approximations. Acta. Math. Hung.6, 241–253 (1955).Google Scholar
  16. 16.
    Turán, P.: On a density theorem of Yu. V. Linnik. Publ. Math. Inst. Hung. Acad. Sci., Ser. A6, 165–179 (1961).Google Scholar
  17. 17.
    —: Analysis and diophantine approximation. Istituto Nazionale di Alta Mathematica. Symposia Mathematica4, 133–153 (1970).Google Scholar

Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • P. X. Gallagher
    • 1
  1. 1.Department of Mathematics Barnard CollegeColumbia UniversityNew YorkUSA

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