On estimates for integral solutions of linear inequalities |
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Authors: | S Raghavan |
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Institution: | (1) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400005 Bombay, India |
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Abstract: | Recently, Bombieri and Vaaler obtained an interesting adelic formulation of the first and the second theorems of Minkowski
in the Geometry of Numbers and derived an effective formulation of the well-known “Siegel’s lemma” on the size of integral
solutions of linear equations. In a similar context involving linearinequalities, this paper is concerned with an analogue of a theorem of Khintchine on integral solutions for inequalities arising from
systems of linear forms and also with an analogue of a Kronecker-type theorem with regard to euclidean frames of integral
vectors. The proof of the former theorem invokes Bombieri-Vaaler’s adelic formulation of Minkowski’s theorem. |
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Keywords: | Bounds for integral solutions of linear inequalities Theorems of Khintchine and of Kronecker-type Bombieri-Vaaler formulation of Minkowski’ s theorems in geometry of numbers Siegel’ s lemma |
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