Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-25T06:14:36.776Z Has data issue: false hasContentIssue false

On the product of two linear forms, one homogeneous and one inhomogeneous

Published online by Cambridge University Press:  09 April 2009

P. E. Blanksby
Affiliation:
Mathematics DepartmentUniversity of Adelaide
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is devoted to a complete investigation into a problem initiated by Davenport [4], and further studied by Kanagasabapathy [6], [7], from whom I borrow the title. The question is a hybrid of the two classical results of Hurwitz and Minkowski on indefinite binary quadratic forms.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Barnes, E. S., The inhomogeneous minima of binary quadratic forms IV, Acta Math. 92 (1954), 235264.CrossRefGoogle Scholar
[2]Barnes, E. S., On linear inhomogenous diophantine approximation, J. London Math. Soc. 31 (1956), 7379.CrossRefGoogle Scholar
[3]Barnes, E. S. and Swinnerton-Dyer, H. P. F., The inhomogeneous minima of binary quadratic forms III, Acta Math. 92 (1954), 199234.CrossRefGoogle Scholar
[4]Davenport, H., On a result of Chalk, Quart. J. Math. Oxford Ser. (2) 4 (1952), 130138.CrossRefGoogle Scholar
[5]Delauney, B. M., An algorithm for the divided cell of a lattice, Izvestia Acad. Nauk. SSSR 11 (1947), 505538 (in Russian).Google Scholar
[6]Kanagasabapathy, P., On the product of two linear forms, one homogeneous and one inhomogeneous, Quart. J. Math. Oxford Ser. (2) 3 (1952). 197205.CrossRefGoogle Scholar
[7]Kanagasabapathy, P., On the product (ax+by+c) (dx+ey), Bull. Calcutta Math. Soc. 51 (1959), 17.Google Scholar
[8]Pitman, E. J., Ph. D. Thesis, University of Sydney, Australia (1957).Google Scholar
[9]Pitman, E. J., The inhomogeneous minima of a sequence of symmetric Markov forms, Acta Arith. 5 (1958), 81116.CrossRefGoogle Scholar