Counting Diophantine Approximations
Brüdern, Jörg
Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, p. 237-260 / Harvested from Project Euclid
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A recent development of the Davenport-Heilbronn method for diophantine inequalities is reexamined, and then applied to a class of problems in diophantine approximation. Among other things, an asymptotic formula is obtained for the number of solutions of the simultaneous inequalities $|n_j - \lambda_j n_0| <\varepsilon$ with square-free $n_j \in [1,N]$, whenever the positive real numbers $\lambda_1, \ldots, \lambda_r$ and $1$ are linearly independent over the rationals.
Publié le : 2008-12-15
Classification:  Davenport-Heilbronn method,  diophantine approximation,  square-free numbers,  11J13,  11D75 
@article{1229696574,
     author = {Br\"udern, J\"org},
     title = {Counting Diophantine Approximations},
     journal = {Funct. Approx. Comment. Math.},
     volume = {38},
     number = {1},
     year = {2008},
     pages = { 237-260},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229696574}
}

Brüdern, Jörg. Counting Diophantine Approximations. Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, pp.  237-260. http://gdmltest.u-ga.fr/item/1229696574/