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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, [email protected]
TREVOR D. WOOLEY
Affiliation:
Department of Mathematics, University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, MI 48109-1109, [email protected]
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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

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