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The asymptotics of points of bounded height on diagonal cubic and quartic threefolds. (English) Zbl 1143.14300
Hess, Florian (ed.) et al., Algorithmic number theory. 7th international symposium, ANTS-VII, Berlin, Germany, July 23–28, 2006. Proceedings. Berlin: Springer (ISBN 3-540-36075-1/pbk). Lecture Notes in Computer Science 4076, 317-332 (2006).
Summary: For the families $$ax^{3}=by^{3} + z^{3} + v^{3} + w^{3}, a, b = 1,\ldots ,100$$, and $$ax^{4} = by^{4} + z^{4} + v^{4} + w^{4}, a, b = 1,\ldots ,100$$, of projective algebraic threefolds, we test numerically the conjecture of Manin (in the refined form due to Peyre) about the asymptotics of points of bounded height on Fano varieties.
For the entire collection see [Zbl 1103.11002].

MSC:
 14G05 Rational points 11G35 Varieties over global fields 11G50 Heights
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