Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T06:54:08.491Z Has data issue: false hasContentIssue false
  • English
  • Français

A diophantine inequality with prime variables

Published online by Cambridge University Press:  17 April 2009

S. Srinivasan
S. Srinivasan
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India
Rights & Permissions [Opens in a new window]

Abstract

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.

Let λ1, λ2, λ3 be non-zero reals, not all of the same sign and such that at least one ratio λi/λj is irrational. Then it is proved that for any given integer k ≥ 1 and real η, the inequaltiy

is solvable for every ε > 0. More general and sharper results are also proved.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 1 , August 1988 , pp. 57 - 66
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Bambah, R.P., ‘Four squares and a kth power’, Quart. J. Math. 5 (1954), 191–202.CrossRefGoogle Scholar
[2]Danicic, J., ‘On the integral part of a linear form with prime variables’, Canad. J. Math. 18 (1966), 821–628.Google Scholar
[3]Hua, L.K., Additive theory of prime numbers (A.M.S., Providence, Rhode Island, 1965).Google Scholar
[4]Vaughan, R.C., ‘Diophantine approximations by prime numbers I’, Proc. London Math. Soc. (3) 28 (1974), 373–384.CrossRefGoogle Scholar
[5]Vaughan, R.C., ‘Diophantine approximations by prime numbers II’, Proc. London Math. Soc. (3) 28 (1974), 385–401.CrossRefGoogle Scholar