login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A278790 Number of real cubic fields with discriminant <= 10^n. 2
0, 2, 27, 382, 4804, 54600, 592922, 6248290, 64659361, 661448081, 6715824025 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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 real cubic fields with discriminant <= X is asymptotic to X/(12*zeta(3)) = (0.069325...)*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.
REFERENCES
Henri Cohen, Advanced Topics in Computational Number Theory, Springer, 2000, p. 426 (and Chapter 8 more generally).
LINKS
Karim Belabas, A fast algorithm to compute cubic fields, Math. Comp. 66 (1997), 1213-1237.
Manjul Bhargava, Arul Shankar, Jacob Tsimerman, On the Davenport-Heilbronn theorems and second order terms, Invent. math. 193:2 (2013) 439-499.
David P. Roberts, Density of cubic field discriminants, Math. Comp. 70 (2001), 1699-1705.
CROSSREFS
Sequence in context: A091709 A083384 A121971 * A277832 A221674 A363961
KEYWORD
nonn,more
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)