Abstract
Let Гr,n—r denote the infimum of all number Г > 0 such that for any real indefinite quadratic form inn variables of type (r, n—r), determinantD ≠ 0 and real numbers c1; c2,…, cn, there exist integersx 1,x2,…,xn satisfying 0 < Q(x1+c1,x2 + c2,…,xn + cn) ≤(Г¦Z > ¦)1/n. All the values of Гr,n—r are known except for г1,4. Earlier it was shown that 8 ≤Г1,4 ≤16. Here we improve the upper bound to get Г1,4 < 12.
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Raka, M., Rani, U. Positive values of non-homogeneous indefinite quadratic forms of type (1, 4). Proc. Indian Acad. Sci. (Math. Sci.) 107, 329–361 (1997). https://doi.org/10.1007/BF02837219
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DOI: https://doi.org/10.1007/BF02837219