{"product_id":"the-lifted-root-number-conjecture-andreas-nickel-9783832519698","title":"The Lifted Root Number Conjecture for Small Sets of Places and an Application to CM-Extensions","description":"In this paper we study a famous conjecture which relates the leading terms at zero of Artin L-functions attached to a finite Galois extension L\/K of number fields to natural arithmetic invariants. This conjecture is called the Lifted Root Number Conjecture (LRNC) and has been introduced by K.W.Gruenberg, J.Ritter and A.Weiss; it depends on a set S of primes of L which is supposed to be sufficiently large. We formulate a LRNC for small sets S which only need to contain the archimedean primes. We apply this to CM-extensions which we require to be (almost) tame above a fixed odd prime p. In this case the conjecture naturally decomposes into a plus and a minus part, and it is the minus part for which we prove the LRNC at p for an infinite class of relatively abelian extensions. Moreover, we show that our results are closely related to the Rubin-Stark conjecture.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Andreas Nickel\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3832519696\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783832519698\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Logos Verlag Berlin\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/15\/2008\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 102\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback","brand":"Andreas Nickel","offers":[{"title":"Paperback","offer_id":48450118222079,"sku":"9783832519698","price":50.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_cb8f93d5-4e1e-4ffb-aee0-1d47bb1ccaba.jpg?v=1777266293","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-lifted-root-number-conjecture-andreas-nickel-9783832519698","provider":"WR Book House","version":"1.0","type":"link"}