• Positive values of non-homogeneous indefinite quadratic forms of type (1, 4)

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      https://www.ias.ac.in/article/fulltext/pmsc/107/04/0329-0361

    • Keywords

       

      Equivalent forms; reduction; soluble

    • 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 integersx1,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.

    • Author Affiliations

       

      Madhu Raka1 Urmila Rani1

      1. Department of Mathematics, Panjab University, Chandigarh - 160014, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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