{"product_id":"9783832519698","title":"The Lifted Root Number Conjecture for small sets of places and an application to CM-extensions","description":"\u003cp\u003eIn 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.\u003c\/p\u003e","brand":"Logos Verlag","offers":[{"title":"Default Title","offer_id":47058155307248,"sku":"9783832519698","price":50.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9783832519698_p0.jpg?v=1763687332","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9783832519698","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}