TY - JOUR

T1 - Products of matrices [1 0 11] and the distribution of reduced quadratic irrationals

AU - Boca, Florin P.

PY - 2007/6/27

Y1 - 2007/6/27

N2 - Let (N) denote the number of products of matrices and of trace equal to N, and be the number of such products of trace at most N. We prove an asymptotic formula of type as N → ∞. As a result, the Dirichlet series has a meromorphic extension in the half-plane with a single, order two pole at s = 2. Our estimate also improves on an asymptotic result of Faivre concerning the distribution of reduced quadratic irrationals, providing an explicit upper bound for the error term.

AB - Let (N) denote the number of products of matrices and of trace equal to N, and be the number of such products of trace at most N. We prove an asymptotic formula of type as N → ∞. As a result, the Dirichlet series has a meromorphic extension in the half-plane with a single, order two pole at s = 2. Our estimate also improves on an asymptotic result of Faivre concerning the distribution of reduced quadratic irrationals, providing an explicit upper bound for the error term.

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U2 - 10.1515/CRELLE.2007.038

DO - 10.1515/CRELLE.2007.038

M3 - Article

AN - SCOPUS:34547818141

SP - 149

EP - 165

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

SN - 0075-4102

IS - 606

ER -