Abstract
For the families ax 3 = by 3 + z 3 + v 3 + w 3, a, b = 1, ... ,100, and ax 4 = by 4 + z 4 + v 4 + w 4, a, b = 1, ... ,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.
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Elsenhans, AS., Jahnel, J. (2006). The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_23
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DOI: https://doi.org/10.1007/11792086_23
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