Correction to: Fourier uniformity of bounded multiplicative functions in short intervals on average
نویسندگان
چکیده
منابع مشابه
Multiplicative Functions in Short Intervals
We introduce a general result relating “short averages” of a multiplicative function to “long averages” which are well understood. This result has several consequences. First, for the Möbius function we show that there are cancellations in the sum of μ(n) in almost all intervals of the form [x, x+ψ(x)] with ψ(x)→∞ arbitrarily slowly. This goes beyond what was previously known conditionally on t...
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1. Statement of the principal result. The class of sequences obtainable as Fourier coefficients of measures on the circle group presents numerous structure problems of interest. Amongst the earliest results somewhat akin to that stated below appear Banach's theorems about lacunary coefficients; see e.g., [4, pp. 215-220]. More recently Helson [3] has studied analogous questions when the group c...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2019
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-019-00931-z