Class number one problem for real quadratic fields of a certain type
Kostadinka Lapkova (2012)
Acta Arithmetica
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Kostadinka Lapkova (2012)
Acta Arithmetica
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Larry J. Gerstein (2000)
Acta Arithmetica
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L. Szczepanik (1978)
Colloquium Mathematicae
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M. Kula, L. Szczepanik, K. Szymiczek (1979)
Manuscripta mathematica
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Sheng Chen, Hong You (2003)
Acta Arithmetica
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Toru Komatsu (2002)
Acta Arithmetica
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Mireille Car (2008)
Acta Arithmetica
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Radan Kučera (2010)
Acta Arithmetica
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Iwao Kimura (2003)
Acta Arithmetica
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Yoonjin Lee (2006)
Acta Arithmetica
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András Biró, Kostadinka Lapkova (2016)
Acta Arithmetica
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We solve unconditionally the class number one problem for the 2-parameter family of real quadratic fields ℚ(√d) with square-free discriminant d = (an)²+4a for positive odd integers a and n.
Mark Coleman, Andrew Swallow (2005)
Acta Arithmetica
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R.W. Davis (1976)
Journal für die reine und angewandte Mathematik
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Manabu Murata (2006)
Acta Arithmetica
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Mireille Car (2004)
Acta Arithmetica
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Takashi Agoh, Toshiaki Shoji (1998)
Monatshefte für Mathematik
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Konrad Jałowiecki, Przemysław Koprowski (2016)
Banach Center Publications
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This paper presents algorithms for quadratic forms over a formally real algebraic function field K of one variable over a fixed real closed field k. The algorithms introduced in the paper solve the following problems: test whether an element is a square, respectively a local square, compute Witt index of a quadratic form and test if a form is isotropic/hyperbolic. Finally, we remark on a method for testing whether two function fields are Witt equivalent.
Iwao Kimura (2004)
Acta Arithmetica
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Lerna Pehlivan, Kenneth S. Williams (2015)
Acta Arithmetica
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Toru Komatsu (2001)
Acta Arithmetica
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