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Keywords:
Weyl sum; indefinite integral binary quadratic form; real quadratic field; geodesic; asymptotic distribution
Weyl sum; indefinite integral binary quadratic form; real quadratic field; geodesic; asymptotic distribution
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.
References:
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[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 10.1093/imrn/rnr112 | MR 2926988 | Zbl 1300.11086
[3] Iwaniec, H., Kowalski, E.: Analytic Number Theory. American Mathematical Society Colloquium Publications 53, American Mathematical Society, Providence (2004). DOI 10.1090/coll/053 | MR 2061214 | Zbl 1059.11001
[4] Murty, M. R.: Problems in Analytic Number Theory. Graduate Texts in Mathematics 206, Springer, New York (2008). DOI 10.I007/978-1-4757-3441-6 | MR 1803093 | Zbl 1190.11001
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