Primitive representation of a binary quadratic form as a sum of four squares
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John Hunsucker (1971)
Acta Arithmetica
Eva Bayer-Fluckiger (1987)
Journal für die reine und angewandte Mathematik
Antoine Ducros (1996)
Manuscripta mathematica
Roger Ware, Ján Minác (1992)
Mathematische Annalen
D.G. James (1980)
Journal für die reine und angewandte Mathematik
MacDonald, Mark L. (2009)
Documenta Mathematica
Ahmet Tekcan (2007)
Applications of Mathematics
In this paper we consider proper cycles of indefinite integral quadratic forms with discriminant . We prove that the proper cycles of can be obtained using their consecutive right neighbors for . We also derive explicit relations in the cycle and proper cycle of when the length of the cycle of is odd, using the transformations and .
Daniel Duverney (1996)
Journal für die reine und angewandte Mathematik
Marc-Hubert Nicole, Adrian Vasiu, Torsten Wedhorn (2010)
Annales scientifiques de l'École Normale Supérieure
Let be a field of characteristic . Let be a over (i.e., an -truncated Barsotti–Tate group over ). Let be a -scheme and let be a over . Let be the subscheme of which describes the locus where is locally for the fppf topology isomorphic to . If , we show that is pure in , i.e. the immersion is affine. For , we prove purity if satisfies a certain technical property depending only on its -torsion . For , we apply the developed techniques to show that all level ...
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