Geodesic
On the generalized Roth–Schmidt theorem
Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part II, Tome 134 (1984), pp. 226-231 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

It is proved that the inequality $$ \prod_{i=1}^{n-1}\|q\theta_i\|<c(qf(q))^{-1}, $$ where $c$ is a fixed constant, $f(q)>\log q$ and $\theta_1,\dots,\theta_{n-1}$ belong to a totally real algebraic number field of degree $n$ can be solved for arbitrary large $q$. For $n=3$ necessary and sufficient conditions are given in order that $f(q)=O(\log q)$. 
@article{ZNSL_1984_134_a11,
     author = {B. F. Skubenko},
     title = {On the generalized {Roth{\textendash}Schmidt} theorem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {226--231},
     year = {1984},
     volume = {134},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a11/}
}
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B. F. Skubenko. On the generalized Roth–Schmidt theorem. Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part II, Tome 134 (1984), pp. 226-231. http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a11/