COHEN, Henri; RUBINSTEIN-SALZEDO, Simon; THORNE, Frank

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COHEN, Henri
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]

RUBINSTEIN-SALZEDO, Simon
Department of Statistics [Stanford]

THORNE, Frank
Department of Mathematics [Columbia]

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Article de revue

Este ítem está publicado en

Compositio Mathematica. 2015, vol. 151, n° 11, p. 2059-2075

Foundation Compositio Mathematica

Resumen en inglés

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.< Leer menos

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https://oskar-bordeaux.fr/handle/20.500.12278/194482

Proyecto europeo

Algorithmic Number Theory in Computer Science

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Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251