Identitites for Field Extensions Generalizing the Ohno–Nakagawa Relations
COHEN, Henri
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
COHEN, Henri
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Language
en
Article de revue
This item was published in
Compositio Mathematica. 2015, vol. 151, n° 11, p. 2059-2075
Foundation Compositio Mathematica
English Abstract
In previous work, Ohno [Ohn97] conjectured, and Nakagawa [Nak98] proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, ...Read more >
In previous work, Ohno [Ohn97] conjectured, and Nakagawa [Nak98] proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them as consequences of 'extra functional equations' involving the Shintani zeta functions associated to the prehomogeneous vector space of binary cubic forms. In the present paper we generalize their result by proving a similar identity relating certain degree fields with Galois groups D and F respectively, for any odd prime, and in particular we give another proof of the Ohno–Nakagawa relation without appealing to binary cubic forms.Read less <
European Project
Algorithmic Number Theory in Computer Science
Origin
Hal imported