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Multiplicative Number Theory pp 126–131Cite as

Siegel’s Theorem

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Part of the book series: Graduate Texts in Mathematics ((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)

.

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References

  1. Acta Arithmetica, 1, 83–86 (1935).

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  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.

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  3. Math. Zeitschrift, 37, 405–415 (1933).

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  12. Ann. Math., 94, 139–152, 153–173 (1971).

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  13. 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).

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Authors and Affiliations

  1. Cambridge University, Cambridge, England

    Harold Davenport

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  1. Harold Davenport
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© 1980 Ann Davenport

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Davenport, H. (1980). Siegel’s Theorem. In: Multiplicative Number Theory. Graduate Texts in Mathematics, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5927-3_21

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  • DOI: https://doi.org/10.1007/978-1-4757-5927-3_21

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-5929-7

  • Online ISBN: 978-1-4757-5927-3

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