Systems of quadratic diophantine inequalities
Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 217-236.

Soient Q 1 ,...,Q r des formes quadratiques avec des coefficients réels. Nous prouvons que pour chaque ε>0 le système |Q 1 (x)|<ε,...,|Q r (x)|<ε des inégalités a une solution entière non-triviale si le système Q 1 (x)=0,...,Q r (x)=0 a une solution réelle non-singulière et toutes les formes i=1 r α i Q i , α=(α 1 ,...,α r ) s ,α0 sont irrationnelles avec rang >8r.

Let Q 1 ,,Q r be quadratic forms with real coefficients. We prove that for any ϵ>0 the system of inequalities |Q 1 (x)|<ϵ,,|Q r (x)|<ϵ has a nonzero integer solution, provided that the system Q 1 (x)=0,,Q r (x)=0 has a nonsingular real solution and all forms in the real pencil generated by Q 1 ,,Q r are irrational and have rank >8r.

@article{JTNB_2005__17_1_217_0,
     author = {Wolfgang M\"uller},
     title = {Systems of quadratic diophantine inequalities},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {217--236},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {1},
     year = {2005},
     doi = {10.5802/jtnb.488},
     zbl = {1082.11020},
     mrnumber = {2152222},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.488/}
}
Wolfgang Müller. Systems of quadratic diophantine inequalities. Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 217-236. doi : 10.5802/jtnb.488. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.488/

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