V. I. Bernik, A. V. Ustinov, “On the distribution of points on the modular hyperbola”, Dal'nevost. Mat. Zh., 2014, Volume 14, Number 2,Pages <nobr>141

This article is cited in 2 papers

On the distribution of points on the modular hyperbola

V. I. Bernik^a, A. V. Ustinov^b

^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 $\bigl|\begin{smallmatrix} a & x\\ y & z \end{smallmatrix}\bigr|=q$ 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.

UDC: 511.336, 511.335

MSC: Primary 11L05; Secondary 11D45

Received: 16.09.2014