On the solutions of quadratic Diophantine equations
Documenta mathematica, Tome 15 (2010), pp. 347-385.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: We determine a finite set of representatives of the set of local solutions in a maximal lattice modulo the stabilizer of the lattice in question for a quadratic Diophantine equation. Our study is based on the works of Shimura on quadratic forms, especially citeSh3 and citeSh4. Indeed, as an application of the result, we present a criterion (in both global and local cases) of the maximality of the lattice of $(11.6\textrm{a} )$ in citeSh3. This gives an answer to the question $(11.6\textrm{a} )$. As one more global application, we investigate primitive solutions contained in a maximal lattice for the sums of squares on each vector space of dimension $4, 6, 8$, or $10$ over the field of rational numbers.
Classification : 11D09, 11E08, 11E12
Mots-clés : maximal lattices, quadratic Diophantine equations 
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     author = {Yoshinaga, Takashi},
     title = {On the solutions of quadratic {Diophantine} equations},
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Yoshinaga, Takashi. On the solutions of quadratic Diophantine equations. Documenta mathematica, Tome 15 (2010), pp. 347-385. https://geodesic-test.mathdoc.fr/item/DOCMA_2010__15__a24/