Hua's lemma and simultaneous diagonal equations

J Brudern, TD Wooley

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)


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)2(k-2). By way of comparison, classical methods based on the use of Hua's lemma would establish a similar conclusion, provided instead that s > r2(k).
Translated title of the contributionHua's lemma and simultaneous diagonal equations
Original languageEnglish
Pages (from-to)279 - 283
Number of pages5
JournalBulletin of the London Mathematical Society
Volume34 (3)
Publication statusPublished - May 2002

Bibliographical note

Publisher: London Math Soc


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