Dirichlet Structure Constant

 kappa(d)={(2lneta(d))/(sqrt(d))   for d>0; (2pi)/(w(d)sqrt(|d|))   for d<0,

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.

See also

Class Number, Dirichlet L-Series, Fundamental Unit

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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.

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Dirichlet Structure Constant

Cite this as:

Weisstein, Eric W. "Dirichlet Structure Constant." From MathWorld--A Wolfram Web Resource.

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