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HUA'S LEMMA AND SIMULTANEOUS DIAGONAL EQUATIONS
Published online by Cambridge University Press: 22 May 2002
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.
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- © The London Mathematical Society 2002
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