Mathematics – Number Theory
Scientific paper
2007-07-23
Mathematics
Number Theory
Minor changes. Final version to appear in proceedings of the conference on the occasion of Sunada's 60th birthday. Contemp.Mat
Scientific paper
We study a variant of a problem considered by Dinaburg and Sinai on the statistics of the minimal solution to a linear Diophantine equation. We show that the signed ratio between the Euclidean norms of the minimal solution and the coefficient vector is uniformly distributed modulo one. We reduce the problem to an equidistribution theorem of Anton Good concerning the orbits of a point in the upper half-plane under the action of a Fuchsian group.
Risager Morten S.
Rudnick Zeev
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