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

Published online by Cambridge University Press:  29 March 2012

KAISA MATOMÄKI
KAISA MATOMÄKI*
Affiliation:
Department of Mathematics, University of Turku, 20014 Turku, Finland e-mail: ksmato@utu.fi
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Abstract

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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.

Keywords

11F3011J2511N25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 2 , May 2012 , pp. 381 - 397
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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