Generalized Perron Identity for broken lines
;
Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 1, pp. 131-144.

In this paper, we generalize the Perron Identity for Markov minima. We express the values of binary quadratic forms with positive discriminant in terms of continued fractions associated to broken lines passing through the points where the values are computed.

Dans cet article, nous généralisons l’identité de Perron pour les minima de Markov. Nous exprimons les valeurs des formes quadratiques binaires à discriminant positif en termes des fractions continues associées aux lignes brisées passant par les points où les valeurs sont calculées.

Received: 2018-02-02
Revised: 2018-06-29
Accepted: 2018-07-16
Published online: 2019-07-29
DOI: https://doi.org/10.5802/jtnb.1071
Classification: 11J06,  11H55
Keywords: Geometry of continued fractions, Perron Identity, binary quadratic indefinite form
@article{JTNB_2019__31_1_131_0,
     author = {Oleg Karpenkov and Matty van-Son},
     title = {Generalized Perron Identity for broken lines},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {31},
     number = {1},
     year = {2019},
     pages = {131-144},
     doi = {10.5802/jtnb.1071},
     language = {en},
     url={jtnb.centre-mersenne.org/item/JTNB_2019__31_1_131_0/}
}
Karpenkov, Oleg; van-Son, Matty. Generalized Perron Identity for broken lines. Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 1, pp. 131-144. doi : 10.5802/jtnb.1071. https://jtnb.centre-mersenne.org/item/JTNB_2019__31_1_131_0/

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