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Israel Journal of Mathematics

, Volume 14, Issue 1, pp 39–49 | Cite as

A large sieve for a class of non-abelianL-functions

  • Morris Goldfeld
Article

Abstract

Letq be a fixed odd prime. We consider the sequence of Kummer fields\(Q\left( {\mathop \surd \limits^q 1,\mathop {\surd a}\limits^q } \right)\) asa varies. Estimates are given for the global density of zeroes of ArtinL-functions of these fields. These results are obtained by deducing a series representation for the ArtinL-functions that arises naturally in the arithmetic ofQ.

Keywords

Galois Group Dirichlet Character Primitive Character Rational Integer Ground Field 
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References

  1. 1.
    E. Artin,Ueber eine neu art von L-reihen, Abh. Math. Sem. Univ. Hamburg3 (1923), 89–108.CrossRefGoogle Scholar
  2. 2.
    E. Artin,Zur theorie der L-reihen mit allgemeinen gruppencharakteren, Abh. Math. Sem. Univ. Hamburg8 (1930), 292–306.zbMATHGoogle Scholar
  3. 3.
    E. Bombieri,On the large sieve, Mathematika12 (1965), 201–225.MathSciNetzbMATHGoogle Scholar
  4. 4.
    R. Brauer,On Artin’s L-series, with general group characters, Ann. of Math. (2)48 (1947), 502–514.CrossRefMathSciNetGoogle Scholar
  5. 5.
    J. W. Cassels and A. Frohlich,Algebraic Number Theory, Proceedings of the Brighton Conference, Academic Press, New York, 1968.Google Scholar
  6. 6.
    E. Fogels,On the zeros of L-functions, Acta Arith.11 (1965), 67–96.zbMATHMathSciNetGoogle Scholar
  7. 7.
    P. X. Gallagher,A large sieve density estimate near σ=1 Invent. Math.11 (1970), 329–339.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    M. Goldfeld,Artin’s conjecture on the average, Mathematika15 (1968), 223–226.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    H. L. Montgomery,Zeros of L-functions, Invent. Math.8 (1969), 346–354.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    K. Prachar,Primzahlverteilung, Springer, 1967.Google Scholar
  11. 11.
    C. L. Siegel,On the zeros of Dirichlet L-functions, Ann. of Math. (2)46 (1945), 409–422.CrossRefMathSciNetGoogle Scholar
  12. 12.
    P. Turan,On some new theorems in the theory of diophantine approximations, Acta. Math. Acad. Sci. Hungar.6 (1955), 241–253.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1973

Authors and Affiliations

  • Morris Goldfeld
    • 1
  1. 1.Department of MathematicsTel Aviv UniversityTel AvivIsrael

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