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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
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Category: math
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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
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Date available: 2019-05-24T08:59:21Z
Last updated: 2019-09-26
Stable URL: http://hdl.handle.net/10338.dmlcz/147737
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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
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