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ON THE DISTRIBUTION OF B-FREE NUMBERS AND NON-VANISHING FOURIER COEFFICIENTS OF CUSP FORMS
Tekijät: Matomaki K
Kustantaja: CAMBRIDGE UNIV PRESS
Julkaisuvuosi: 2012
Journal: Glasgow Mathematical Journal
Tietokannassa oleva lehden nimi: GLASGOW MATHEMATICAL JOURNAL
Lehden akronyymi: GLASGOW MATH J
Numero sarjassa: 2
Vuosikerta: 54
Numero: 2
Aloitussivu: 381
Lopetussivu: 397
Sivujen määrä: 17
ISSN: 0017-0895
DOI: https://doi.org/10.1017/S0017089512000043
Tiivistelmä
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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