Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-19T07:07:57.767Z Has data issue: false hasContentIssue false

On simultaneous additive equations, III

Published online by Cambridge University Press:  26 February 2010

Trevor D. Wooley
Affiliation:
Department of Mathematics, Imperial College, Queen's Gate, London, SW7 2BZ
Get access

Extract

Let ci, and di, (1≤i≤s) be rational integers, and k and n be natural numbers. We shall consider the solubility over the p-adic integers ℤp of the pair of additive equations

Type
Research Article
Copyright
Copyright © University College London 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Atkinson, O. D. and Cook, R. J.. Pairs of additive congruences to a large prime modulus. J. Austral. Math. Soc, 46A (1989), 438455.CrossRefGoogle Scholar
2.Chowla, S., Mann, H. B. and Straus, E. G.. Some applications of the Cauchy-Davenport theorem. Kon. Norske Vidensk. Selsk. Fork, 32 (1959), 7480.Google Scholar
3.Davenport, H. and Lewis, D. J.. Cubic equations of additive type. Phil. Trans. Roy. Soc. Lond., 261A (1966), 97136.Google Scholar
4.Davenport, H. and Lewis, D. J.. Two additive equations. Proc. Symp. in Pure Math., Vol. XII (Houston, Tex., 1967), 7498.Google Scholar
5.Davenport, H. and Lewis, D. J.. Simultaneous equations of additive type. Phil. Trans. Roy. Soc. Lond., 264A (1969), 557595.Google Scholar
6.Dodson, M. M.. Homogeneous additive congruences. Phil. Trans. Roy. Soc. Lond., 261A (1966), 163210.Google Scholar
7.Greenberg, M. J.. Lectures on forms in many variables (W. A. Benjamin, Inc., New York, Amsterdam, 1969).Google Scholar
8.Schmidt, W. M.. Equations over finite fields. An elementary approach. Lecture Notes in Mathematics, 536 (Springer-Verlag, Berlin, 1976).CrossRefGoogle Scholar
9.Wooley, T. D.. On simultaneous additive equations I. Submitted for publication.Google Scholar