The size function for quadratic extensions of complex quadratic fields
Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 1, pp. 243-259.

The function h 0 for a number field is an analogue of the dimension of the Riemann–Roch spaces of divisors on an algebraic curve. In this paper, we prove the conjecture of van der Geer and Schoof about the maximality of h 0 at the trivial Arakelov divisor for quadratic extensions of complex quadratic fields.

La fonction h 0 pour un corps de nombre est un analogue de la dimension des espaces vectoriels de Riemann–Roch des diviseurs sur une courbe algébrique. Dans cet article, nous montrons une conjecture de van der Geer et Schoof sur la maximalité de h 0 au diviseur d’Arakelov trivial pour les extensions quadratiques de corps quadratiques imaginaires.

Received:
Accepted:
Published online:
DOI: 10.5802/jtnb.978
Classification: 11R16, 11R11, 11R55, 11R40
Keywords: Arakelov divisor, effectivity divisor, size function, $h^0$, line bundle
Tran, Ha Thanh Nguyen 1

1 Department of Mathematics and Systems Analysis, Aalto University School of Science, Otakaari 1, 02150 Espoo, Finland
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Tran, Ha Thanh Nguyen. The size function for quadratic extensions of complex quadratic fields. Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 1, pp. 243-259. doi : 10.5802/jtnb.978. http://archive.numdam.org/articles/10.5802/jtnb.978/

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