The Class Number Formula relates several fundamental invariants of an algebraic number field, including its class number, regulator, and number of roots of unity, to a specific value of the field's own Dedekind zeta function. It is one of the central bridges between the arithmetic of a number field and the analytic behavior of its zeta function, generalizing simpler formulas already known for the field of rational numbers.
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Proof Year1839 is Dirichlet's proof for quadratic fields only, stated in the language of quadratic forms; the source gives no year for the general formula. StatementRelates many important invariants of an algebraic number field, including its class number, regulator, number of roots of unity and discriminant, to a special value of its Dedekind zeta function. 1 Classification
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Source Class number formula (Wikipedia)
Sources
1. Class number formula (Wikipedia)
Introduction
the class number formula relates many important invariants of an algebraic number field to a special value of its Dedekind zeta function
Dirichlet class number formula
published a proof of the class number formula for quadratic fields in 1839
Proved By: Peter Gustav Lejeune Dirichlet, Lead
Peter Gustav Lejeune Dirichlet published a proof of the class number formula for quadratic fields in 1839, but it was stated in the language of quadratic forms rather than classes of ideals.
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