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Siegel’s Theorem

  • Harold Davenport
Part of the Graduate Texts in Mathematics book series (GTM, volume 74)

Abstract

Siegel’s theorem,1 in the first of its two forms, states that: For any ε > 0 there exists a positive number C 1(ε) such that, if χ is a real primitive character to the modulus q, then
$$ L(1,\chi)>{C_1}(\varepsilon){q^{- \varepsilon}} $$
(1)
.

Keywords

Modular Function Real Zero Riemann Hypothesis Algebraic Number Field Generalize Riemann Hypothesis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Acta Arithmetica, 1, 83–86 (1935).Google Scholar
  2. 2.
    See Landau, Göttinger Nachrichten, 1918, 285–295. The same argument allows one to deduce the first form of Siegel’s theorem from the second.Google Scholar
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    J. London Math. Soc., 23, 275–279 (1948). Other simple proofs have been given by Chowla, Annals of Math. (2) 51, 120–122 (1950) and by Goldfeld, Proc. Nat. Acad. Sci. U.S.A., 71, 1055 (1974).Google Scholar
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    Quarterly J. of Math., 9, 194–195 (1938).Google Scholar

Copyright information

© Ann Davenport 1980

Authors and Affiliations

  • Harold Davenport
    • 1
  1. 1.Cambridge UniversityCambridgeEngland

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