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arXiv · 1503.02370

Linear Equations with Rational Fractions of Bounded Height and Stochastic Matrices

Igor E. Shparlinski
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Abstract

We obtain a tight, up to a logarithmic factor, upper bound on the number of solutions to the equation $$ \sum_{j=1}^n a_j \frac{s_j}{r_j} =a_0, \qquad $$ with variables $r_1,...,r_n$ in an arbitrary box at the origin and variables $s_1,..., s_n$ in an essentially arbitrary translation of this box. We apply this result to get an upper bound on the number of stochastic matrices with rational entries of bounded height.

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Igor E. Shparlinski. 2015-03-09. Linear Equations with Rational Fractions of Bounded Height and Stochastic Matrices. https://arxiv.org/abs/1503.02370

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