×

Simultaneous diophantine approximation. (English) Zbl 0746.11028

From the author’s summary: “Several existence and effective results for theorems of Dirichlet and Minkowski on simultaneous Diophantine approximation in the homogeneous case (including \(p\)-adic and \(p\)-adic- real mixed cases) are given. ”The paper includes a theorem on a polynomial time algorithm to find integer solutions of such diophantine inequalities based on the \(LLL\)- basis reduction algorithm together with an application of the algorithm in a concrete case.

MSC:

11J13 Simultaneous homogeneous approximation, linear forms
11Y16 Number-theoretic algorithms; complexity
11J61 Approximation in non-Archimedean valuations
11J25 Diophantine inequalities

Citations:

Zbl 0687.10026
PDFBibTeX XMLCite