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

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.

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.

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DOI : https://doi.org/10.5802/jtnb.978
Classification : 11R16,  11R11,  11R55,  11R40
Mots clés : Arakelov divisor, effectivity divisor, size function, h 0 , line bundle
@article{JTNB_2017__29_1_243_0,
     author = {Ha Thanh Nguyen Tran},
     title = {The size function for quadratic extensions of complex quadratic fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {243--259},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {29},
     number = {1},
     year = {2017},
     doi = {10.5802/jtnb.978},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.978/}
}
Ha Thanh Nguyen Tran. The size function for quadratic extensions of complex quadratic fields. Journal de Théorie des Nombres de Bordeaux, Tome 29 (2017) no. 1, pp. 243-259. doi : 10.5802/jtnb.978. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.978/

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