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An analogue of Van der Corput's A 5 ‐process for exponential sums
Author(s) -
Robert O.
Publication year - 2002
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/s0025579300016156
Subject(s) - mathematics , exponent , diophantine equation , exponential function , ninth , combinatorics , mathematical analysis , physics , philosophy , linguistics , acoustics
A diophantine system is studied from which is deduced an analogue of van der Corput's A 5 ‐process in order to bound analytic exponential sums of the form∑ 1 ⩽ m ⩽ Me ( f ( m ) ). The saving has now to be taken to the exponent 1/20 instead of 1/32. Our main application is a “ninth derivative test” for exponential sums which is essential for giving new exponent pairs in [3].