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ON THE DISTRIBUTION OF ![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20160202062141776-0871:S0017089512000043_char1.gif?pub-status=live)
-FREE NUMBERS AND NON-VANISHING FOURIER COEFFICIENTS OF CUSP FORMS
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Published online by Cambridge University Press: 29 March 2012
Abstract
We study properties of -free numbers, that is numbers that are not divisible by any member of a set
. 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
-free numbers and their distribution on almost all short intervals. Results on
-free numbers have implications to non-vanishing Fourier coefficients of cusp forms, so this work also gives information about them.
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 2012
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