Hostname: page-component-848d4c4894-89wxm Total loading time: 0 Render date: 2024-07-07T18:15:45.777Z Has data issue: false hasContentIssue false
  • English
  • Français

HUA'S LEMMA AND SIMULTANEOUS DIAGONAL EQUATIONS

Published online by Cambridge University Press:  22 May 2002

JÖRG BRÜDERN  and
TREVOR D. WOOLEY
JÖRG BRÜDERN
Affiliation:
Mathematisches Institut A, Universität Stuttgart, D-70511 Stuttgart, Germanybruedern@mathematik.uni-stuttgart.de
TREVOR D. WOOLEY
Affiliation:
Department of Mathematics, University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, MI 48109-1109, USAwooley@math.lsa.umich.edu
Get access

Abstract

This paper concerns systems of r homogeneous diagonal equations of degree k in s variables, with integer coefficients. Subject to a suitable non-singularity condition, it is shown that the expected asymptotic formula holds for the number of such systems inside a box [−P,P]s, provided only that s > (3r+1)2k−2. By way of comparison, classical methods based on the use of Hua's lemma would establish a similar conclusion, provided instead that s > r2k.

Type
PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 3 , May 2002 , pp. 279 - 283
Copyright
© The London Mathematical Society 2002

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.)