Geodesic
ON THE DISTRIBUTION OF -FREE NUMBERS AND NON-VANISHING FOURIER COEFFICIENTS OF CUSP FORMS
Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 381-397

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DOI

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.
DOI : 10.1017/S0017089512000043
Mots-clés : 11F30, 11J25, 11N25 
MATOMÄKI, KAISA. ON THE DISTRIBUTION OF -FREE NUMBERS AND NON-VANISHING FOURIER COEFFICIENTS OF CUSP FORMS. Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 381-397. doi: 10.1017/S0017089512000043
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     author = {MATOM\"AKI, KAISA},
     title = {ON {THE} {DISTRIBUTION} {OF} {-FREE} {NUMBERS} {AND} {NON-VANISHING} {FOURIER} {COEFFICIENTS} {OF} {CUSP} {FORMS}},
     journal = {Glasgow mathematical journal},
     pages = {381--397},
     year = {2012},
     volume = {54},
     number = {2},
     doi = {10.1017/S0017089512000043},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000043/}
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