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HUA'S LEMMA AND SIMULTANEOUS DIAGONAL EQUATIONS

  • JÖRG BRÜDERN (a1) and TREVOR D. WOOLEY (a2)

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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HUA'S LEMMA AND SIMULTANEOUS DIAGONAL EQUATIONS

  • JÖRG BRÜDERN (a1) and TREVOR D. WOOLEY (a2)

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