the well-known analytic class number formula, linking the special value at s=0 of the dedekind zeta function of a number field to its class number and regulator, has been the foundation and prototype for the highly conjectural theory of special values of l-functions for close to two centuries. we will discuss generalizations of the class number formula to the context of equivariant artin l-functions which capture refinements of the brumer-stark and coates-sinnott conjectures. these generalizations relate various algebraic-geometric invariants associated to a global field, e.g. its quillen k-groups and etale cohomology groups, to various special values of its galois-equivariant l-functions. they illustrate the subtle interactions of number theory with complex and p-adic analysis, algebraic geometry, topology and homological algebra.