Geodesic
A note on the distribution of angles associated to indefinite integral binary quadratic forms
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 443-452

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
To each indefinite integral binary quadratic form $Q$, we may associate the geodesic in $\mathbb {H}$ through the roots of quadratic equation $Q(x,1)$. In this paper we study the asymptotic distribution (as discriminant tends to infinity) of the angles between these geodesics and one fixed vertical geodesic which intersects all of them.
To each indefinite integral binary quadratic form $Q$, we may associate the geodesic in $\mathbb {H}$ through the roots of quadratic equation $Q(x,1)$. In this paper we study the asymptotic distribution (as discriminant tends to infinity) of the angles between these geodesics and one fixed vertical geodesic which intersects all of them.
DOI : 10.21136/CMJ.2018.0370-17
Classification : 06B10, 11L15, 62E20
Keywords: Weyl sum; indefinite integral binary quadratic form; real quadratic field; geodesic; asymptotic distribution 
Đokić, Dragan. A note on the distribution of angles associated to indefinite integral binary quadratic forms. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 443-452. doi: 10.21136/CMJ.2018.0370-17
@article{10_21136_CMJ_2018_0370_17,
     author = {{\DJ}oki\'c, Dragan},
     title = {A note on the distribution of angles associated to indefinite integral binary quadratic forms},
     journal = {Czechoslovak Mathematical Journal},
     pages = {443--452},
     year = {2019},
     volume = {69},
     number = {2},
     doi = {10.21136/CMJ.2018.0370-17},
     mrnumber = {3959957},
     zbl = {07088797},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0370-17/}
}
TY  - JOUR
AU  - Đokić, Dragan
TI  - A note on the distribution of angles associated to indefinite integral binary quadratic forms
JO  - Czechoslovak Mathematical Journal
PY  - 2019
SP  - 443
EP  - 452
VL  - 69
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0370-17/
DO  - 10.21136/CMJ.2018.0370-17
LA  - en
ID  - 10_21136_CMJ_2018_0370_17
ER  - 
%0 Journal Article
%A Đokić, Dragan
%T A note on the distribution of angles associated to indefinite integral binary quadratic forms
%J Czechoslovak Mathematical Journal
%D 2019
%P 443-452
%V 69
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0370-17/
%R 10.21136/CMJ.2018.0370-17
%G en
%F 10_21136_CMJ_2018_0370_17

[1] Buell, D. A.: Binary Quadratic Forms. Classical Theory and Modern Computations. Springer, New York (1989). | DOI | MR | JFM

[2] Duke, W., Friedlander, J. B., Iwaniec, H.: Weyl sums for quadratic roots. Int. Math. Res. Not. 2012 (2012), 2493-2549 erratum ibid. 2012 2646-2648 2012. | DOI | MR | JFM

[3] Iwaniec, H., Kowalski, E.: Analytic Number Theory. American Mathematical Society Colloquium Publications 53, American Mathematical Society, Providence (2004). | DOI | MR | JFM

[4] Murty, M. R.: Problems in Analytic Number Theory. Graduate Texts in Mathematics 206, Springer, New York (2008). | DOI | MR | JFM

Cité par Sources :