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HUA‐TYPE ITERATION FOR MULTIDIMENSIONAL WEYL SUMS
Author(s) -
Parsell Scott T.
Publication year - 2012
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579312000034
Subject(s) - mathematics , diophantine equation , dimension (graph theory) , type (biology) , exponential function , class (philosophy) , degree (music) , pure mathematics , exponential type , value (mathematics) , diophantine approximation , discrete mathematics , mathematical analysis , statistics , ecology , physics , artificial intelligence , computer science , acoustics , biology
We develop Weyl differencing and Hua‐type lemmata for a class of multidimensional exponential sums. We then apply our estimates to bound the number of variables required to establish an asymptotic formula for the number of solutions of a system of diophantine equations arising from the study of linear spaces on hypersurfaces. For small values of the degree and dimension, our results are superior to those stemming from the author's earlier work on Vinogradov's mean value theorem.