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A278791
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Number of complex cubic fields with discriminant >= -10^n.
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2
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0, 7, 127, 1520, 17041, 182417, 1905514, 19609185, 199884780, 2024660098, 20422230540
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OFFSET
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1,2
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COMMENTS
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Belabas invented an algorithm to identify all cubic fields with a discriminant bounded by X in essentially linear time, and computed the above values up to a(11).
The number of complex cubic fields with discriminant >= -X is asymptotic to X/(4*zeta(3)) = (0.207976...)*X. The second order term was conjectured by Roberts to be a known constant times X^{5/6}, and this was subsequently proved by Bhargava et al.
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REFERENCES
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Henri Cohen, Advanced Topics in Computational Number Theory, Springer, 2000, p. 426 (and Chapter 8 more generally)
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LINKS
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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