TOPICS
Search

Dirichlet Structure Constant

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
kappa(d)={(2lneta(d))/(sqrt(d)) for d>0; (2pi)/(w(d)sqrt(|d|)) for d<0,
(1)

where eta(d) is the fundamental unit and w(d) is the number of substitutions which leave the binary quadratic form unchanged, given by

w(d)={6 for d=-3; 4 for d=-4; 2 otherwise.
(2)

See also

Class Number, Dirichlet L-Series, Fundamental Unit

Explore with Wolfram|Alpha

References

Cohen, H. A Course in Computational Algebraic Number Theory. New York: Springer-Verlag, 1993.Cohen, H. Advanced Topics in Computational Number Theory. New York: Springer-Verlag, 2000.Cohn, H. Advanced Number Theory. New York: Dover, 1980.

Referenced on Wolfram|Alpha

Dirichlet Structure Constant

Cite this as:

Weisstein, Eric W. "Dirichlet Structure Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DirichletStructureConstant.html

Subject classifications