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Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients
Author(s) -
Granville Andrew,
Ramaré Olivier
Publication year - 1996
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/s0025579300011608
Subject(s) - mathematics , binomial (polynomial) , binomial coefficient , citation , combinatorics , mathematical economics , library science , statistics , computer science
This paper fills what we believe to be a lacuna in the existing literature concerningupper bounds on exponential sums. Although it has always been evident that many ofthe known estimates can be made explicit, it is a non-trivial problem to actually do so.In particular so that the constants involved do not render the explicit estimates useless inpractical applications.We have used the practical bounds that are needed to prove Theorem 1 as motivationfor our results here, though we hope that ...