Abstract.
We introduce a constant γ m,n (D) attached to a central division algebra D over a number field which is a generalization of the Hermite–Rankin constant. Geometrically, γ m,n (D) equals the maximum of minimal twisted heights of rational points of a generalized Brauer–Severi variety. We will deduce a duality result, an analog of Rankin’s inequality and an upper estimate for γ m,n (D).
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Received 23 October 2000; in revised form 8 September 2001
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Watanabe, T. Hermite Constants of Division Algebras. Mh Math 135, 157–166 (2002). https://doi.org/10.1007/s006050200012
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DOI: https://doi.org/10.1007/s006050200012