Bounds for the degrees of CM-fields of class number one
Sofiène Bessassi (2003)
Acta Arithmetica
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Sofiène Bessassi (2003)
Acta Arithmetica
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John Knopfmacher (1985)
Manuscripta mathematica
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W. Narkiewicz, J. Śliwa (1978)
Colloquium Mathematicae
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Joseph Liang (1972)
Acta Arithmetica
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Daqing Wan (1992)
Manuscripta mathematica
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Stéphane R. Louboutin (2007)
Colloquium Mathematicae
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We give a simple proof of the Siegel-Tatuzawa theorem according to which the residues at s = 1 of the Dedekind zeta functions of quadratic number fields are effectively not too small, with at most one exceptional quadratic field. We then give a simple proof of the Brauer-Siegel theorem for normal number fields which gives the asymptotics for the logarithm of the product of the class number and the regulator of number fields.
Dress, Andreas W.M. (1997)
Beiträge zur Algebra und Geometrie
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Sanoli Gun, M. Ram Murty, Purusottam Rath (2012)
Acta Arithmetica
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W. Narkiewicz (1966)
Colloquium Mathematicae
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Roman Marszałek (2005)
Colloquium Mathematicae
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It is shown that the multiplicative independence of Dedekind zeta functions of abelian fields is equivalent to their functional independence. We also give all the possible multiplicative dependence relations for any set of Dedekind zeta functions of abelian fields.
Günter Lettl (2005)
Acta Arithmetica
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John Smith (1975)
Acta Arithmetica
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R. Brauer (1973)
Acta Arithmetica
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S. Lang (1971)
Inventiones mathematicae
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Albrecht Fröhlich (1960)
Mathematische Zeitschrift
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