| Title:
|
A note on the distribution of angles associated to indefinite integral binary quadratic forms (English) |
| Author:
|
Đokić, Dragan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
443-452 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Weyl sum |
| Keyword:
|
indefinite integral binary quadratic form |
| Keyword:
|
real quadratic field |
| Keyword:
|
geodesic |
| Keyword:
|
asymptotic distribution |
| MSC:
|
06B10 |
| MSC:
|
11L15 |
| MSC:
|
62E20 |
| idZBL:
|
Zbl 07088797 |
| idMR:
|
MR3959957 |
| DOI:
|
10.21136/CMJ.2018.0370-17 |
| . |
| Date available:
|
2019-05-24T08:59:21Z |
| Last updated:
|
2021-07-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147737 |
| . |
| Reference:
|
[1] Buell, D. A.: Binary Quadratic Forms. Classical Theory and Modern Computations.Springer, New York (1989). Zbl 0698.10013, MR 1012948, 10.1007/978-1-4612-4542-1 |
| Reference:
|
[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. Zbl 1300.11086, MR 2926988, 10.1093/imrn/rnr112 |
| Reference:
|
[3] Iwaniec, H., Kowalski, E.: Analytic Number Theory.American Mathematical Society Colloquium Publications 53, American Mathematical Society, Providence (2004). Zbl 1059.11001, MR 2061214, 10.1090/coll/053 |
| Reference:
|
[4] Murty, M. R.: Problems in Analytic Number Theory.Graduate Texts in Mathematics 206, Springer, New York (2008). Zbl 1190.11001, MR 1803093, 10.I007/978-1-4757-3441-6 |
| . |
