Abstract
1. Letwhere a > 0, be an indefinite quadratic form, so that d = b2 − 4ac > 0. A classical theorem of Minkowski states that, if (x0, y0) is any pair of real numbers, there are numbers (x, y) congruent (mod 1) to (x0, y0), such thatand, more recently, Davenport has shown that this theorem can be sharpened for certain special f, for instance that it is always possible to satisfy
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