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Dal'nevost. Mat. Zh., 2014, Volume 14, Number 2, Pages 141–155 (Mi dvmg281)  

This article is cited in 2 scientific papers (total in 2 papers)

On the distribution of points on the modular hyperbola

V. I. Bernika, A. V. Ustinovb

a Institute of Mathematics of the National Academy of Sciences of Belarus
b Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: It is known that solutions of determinant equation $|\begin{smallmatrix} a & x
y & z \end{smallmatrix}|=q$ are uniformly distributed. The article contains similar results when the variables satisfy additional restrictions $(a,x)=1$ or $(a,x,y,z)=1$.

Key words: Kloosterman sums, modular hyperbola

Full text: PDF file (157 kB)
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UDC: 511.336, 511.335
MSC: Primary 11L05; Secondary 11D45
Received: 16.09.2014

Citation: V. I. Bernik, A. V. Ustinov, “On the distribution of points on the modular hyperbola”, Dal'nevost. Mat. Zh., 14:2 (2014), 141–155

Citation in format AMSBIB
\Bibitem{BerUst14}
\by V.~I.~Bernik, A.~V.~Ustinov
\paper On the distribution of points on the modular hyperbola
\jour Dal'nevost. Mat. Zh.
\yr 2014
\vol 14
\issue 2
\pages 141--155
\mathnet{http://mi.mathnet.ru/dvmg281}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. A. V. Ustinov, “The distribution of solutions of a determinantal equation”, Sb. Math., 206:7 (2015), 988–1019  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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