Geodesic
$\mathcal{L}$-algorithm for approximating Diophantine systems of linear forms
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 3, Tome 490 (2020), pp. 25-48 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proposed $\mathcal{L}$ - algorithm for constructing an infinite sequence of integer solutions of linear inequality systems of $ d + 1 $ variable. Solutions are obtained using recurrence relations of order $d + 1$. The approach speed is carried out with the diophantine exponent $\theta = \frac {m} {n} - \varrho $ where $ 1 \leq n \leq d $ is the number of inequalities, $ m = d + 1-n $ — the number of free variables and the deviation $ \varrho> 0 $ can be made arbitrarily small due to a suitable choice of the recurrence relation. 
@article{ZNSL_2020_490_a1,
     author = {V. G. Zhuravlev},
     title = {$\mathcal{L}$-algorithm for approximating {Diophantine} systems of linear forms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     year = {2020},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_490_a1/}
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V. G. Zhuravlev. $\mathcal{L}$-algorithm for approximating Diophantine systems of linear forms. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 3, Tome 490 (2020), pp. 25-48. http://geodesic.mathdoc.fr/item/ZNSL_2020_490_a1/

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