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Hua's Lemma and Simultaneous Diagonal Equations
Author(s) -
Brüdern Jörg,
Wooley Trevor D.
Publication year - 2002
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930100889x
Subject(s) - mathematics , diagonal , lemma (botany) , homogeneous , integer (computer science) , singularity , degree (music) , pure mathematics , combinatorics , mathematical analysis , geometry , programming language , ecology , physics , poaceae , computer science , acoustics , biology
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 > (3 r + 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 > r 2 k .