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
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References
Acta Arithmetica, 1, 83–86 (1935).
See Landau, Göttinger Nachrichten, 1918, 285–295. The same argument allows one to deduce the first form of Siegel’s theorem from the second.
Math. Zeitschrift, 37, 405–415 (1933).
J. London Math. Soc., 9, 289–298 (1934).
Quarterly J. of Math., 5, 150–160 (1934).
Quarterly J. of Math., 5, 293–301 (1934).
Mathematika, 13, 204–216 (1966). See also Chapter 5 of Baker, Transcendental Number Theory, Cambridge University Press, 1975.
Michigan Math. J., 14, 1–27 (1967).
Math. Z., 56, 227–252 (1952).
Invent. Math., 5, 169–179 (1968).
J. Number Theory, 1, 16–27 (1969); Modular Functions of One Variable I, Springer-Verlag, Berlin, 1973, pp. 153–174.
Ann. Math., 94, 139–152, 153–173 (1971).
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).
Quarterly J. of Math., 9, 194–195 (1938).
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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
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