Perturbations of Weyl Sums
نویسندگان
چکیده
منابع مشابه
Perturbations of Weyl Sums
Write fk(α;X) = ∑ x6X e(α1x + . . . + αkx ) (k > 3). We show that there is a set B ⊆ [0, 1)k−2 of full measure with the property that whenever (α2, . . . , αk−1) ∈ B and X is sufficiently large, then sup (α1,αk)∈[0,1) |fk(α;X)| 6 X1/2+4/(2k−1). For k > 5, this improves on work of Flaminio and Forni, in which a Diophantine condition is imposed on αk, and the exponent of X is 1−2/(3k(k−1)).
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2015
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnv225