We use the analogy between class groups and even
K
K
-groups of the ring of integers of a number field and āHigher Stickelbergerā ideals within
K
K
-theory to prove an index formula for these ideals in a finite abelian extension of real number fields, which is similar to the classic Stickelberger ideal index formula proved by Iwasawa.
Let k be an imaginary quadratic number field, and F/k a finite abelian extension of Galois group G. We show that a Gross conjecture concerning the leading terms of Artin L-series holds for F/k and all rational primes which are split in k and which do not divide 6.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citationsācitations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.