{"product_id":"the-lifted-root-number-conjecture-for-small-sets-of-places-and-an-application-to-cm-extensions-paperback","title":"The Lifted Root Number Conjecture for Small Sets of Places and an Application to CM-Extensions - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eAndreas Nickel\u003c\/b\u003e (Author)\u003c\/p\u003e\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\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 102\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.33 x 7.96 x 5.52 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e February 19, 2014\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":46661655068869,"sku":"9783832519698","price":100.6,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0757\/6718\/5605\/files\/QqbusJyjgU9783832519698.webp?v=1785907739","url":"https:\/\/selloorium.com\/products\/the-lifted-root-number-conjecture-for-small-sets-of-places-and-an-application-to-cm-extensions-paperback","provider":"Selloorium","version":"1.0","type":"link"}