A class number formula for higher derivatives of abelian L-functions
Gross and Rubin have made conjectures about special values of equivariant L-functions associated to abelian extensions of global fields. We describe a common refinement, due to Burns, and give evidence in favour of this conjecture for quadratic extensions and cyclotomic fields. We also note that the statement provides a new interpretation of further conjectures of Darmon and Gross.(Received December 24 2002)
(Accepted April 15 2003)
Key Words: abelian L-functions; Rubin–Stark conjecture; Gross's conjecture; cyclotomic fields.
11R42 (primary); 11R29 (secondary).