ON THE DISTRIBUTION OF B-FREE NUMBERS AND NON-VANISHING FOURIER COEFFICIENTS OF CUSP FORMS



: Matomaki K

Publisher: CAMBRIDGE UNIV PRESS

: 2012

: Glasgow Mathematical Journal

: GLASGOW MATHEMATICAL JOURNAL

: GLASGOW MATH J

: 2

: 54

: 2

: 381

: 397

: 17

: 0017-0895

DOI: https://doi.org/10.1017/S0017089512000043


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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