A1 Refereed original research article in a scientific journal
ON THE DISTRIBUTION OF B-FREE NUMBERS AND NON-VANISHING FOURIER COEFFICIENTS OF CUSP FORMS
Authors: Matomaki K
Publisher: CAMBRIDGE UNIV PRESS
Publication year: 2012
Journal: Glasgow Mathematical Journal
Journal name in source: GLASGOW MATHEMATICAL JOURNAL
Journal acronym: GLASGOW MATH J
Number in series: 2
Volume: 54
Issue: 2
First page : 381
Last page: 397
Number of pages: 17
ISSN: 0017-0895
DOI: https://doi.org/10.1017/S0017089512000043
Abstract
We study properties of B-free numbers, that is numbers that are not divisible by any member of a set B. First we formulate the most-used procedure for finding them (in a given set of integers) as easy-to-apply propositions. Then we use the propositions to consider Diophantine properties of B-free numbers and their distribution on almost all short intervals. Results on B-free numbers have implications to non-vanishing Fourier coefficients of cusp forms, so this work also gives information about them.
We study properties of B-free numbers, that is numbers that are not divisible by any member of a set B. First we formulate the most-used procedure for finding them (in a given set of integers) as easy-to-apply propositions. Then we use the propositions to consider Diophantine properties of B-free numbers and their distribution on almost all short intervals. Results on B-free numbers have implications to non-vanishing Fourier coefficients of cusp forms, so this work also gives information about them.
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