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

MATOMÄKI, KAISA

Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 381-397

Résumé

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.

Détail

DOI : 10.1017/S0017089512000043

Mots-clés : 11F30, 11J25, 11N25

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