Systems of quadratic diophantine inequalities
- [1] Institut für Statistik Technische Universität Graz 8010 Graz, Austria
Journal de Théorie des Nombres de Bordeaux (2005)
- Volume: 17, Issue: 1, page 217-236
- ISSN: 1246-7405
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topMüller, Wolfgang. "Systems of quadratic diophantine inequalities." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 217-236. <http://eudml.org/doc/249461>.
@article{Müller2005,
abstract = {Let $Q_1,\dots ,Q_r$ be quadratic forms with real coefficients. We prove that for any $\epsilon >0$ the system of inequalities $|Q_1(x)|<\epsilon ,\dots ,|Q_r(x)|<\epsilon $ has a nonzero integer solution, provided that the system $Q_1(x)=0,\dots ,Q_r(x)=0$ has a nonsingular real solution and all forms in the real pencil generated by $Q_1,\dots ,Q_r$ are irrational and have rank $> 8r$.},
affiliation = {Institut für Statistik Technische Universität Graz 8010 Graz, Austria},
author = {Müller, Wolfgang},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {quadratic forms; Diophantine inequalities; sieve method},
language = {eng},
number = {1},
pages = {217-236},
publisher = {Université Bordeaux 1},
title = {Systems of quadratic diophantine inequalities},
url = {http://eudml.org/doc/249461},
volume = {17},
year = {2005},
}
TY - JOUR
AU - Müller, Wolfgang
TI - Systems of quadratic diophantine inequalities
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 217
EP - 236
AB - Let $Q_1,\dots ,Q_r$ be quadratic forms with real coefficients. We prove that for any $\epsilon >0$ the system of inequalities $|Q_1(x)|<\epsilon ,\dots ,|Q_r(x)|<\epsilon $ has a nonzero integer solution, provided that the system $Q_1(x)=0,\dots ,Q_r(x)=0$ has a nonsingular real solution and all forms in the real pencil generated by $Q_1,\dots ,Q_r$ are irrational and have rank $> 8r$.
LA - eng
KW - quadratic forms; Diophantine inequalities; sieve method
UR - http://eudml.org/doc/249461
ER -
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