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Chebyshevskii Sbornik, 2018, Volume 19, Issue 3, Pages 148–163
DOI: https://doi.org/10.22405/2226-8383-2018-19-3-148-163
(Mi cheb685)
 

This article is cited in 1 scientific paper (total in 1 paper)

Another application of Linnik dispersion method

Étienne Fouvryabc, Maksym Radziwiłłd

a Laboratoire de Mathématiques d'Orsay, Univ. Paris–Sud
b Université Paris–Saclay, 91405 Orsay, France
c CNRS
d Department of Mathematics, McGill University, Burnside Hall, Room 1005, 805 Sherbrooke Street West, Montreal, Quebec, Canada, H3A 0B9
Full-text PDF (696 kB) Citations (1)
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Abstract: Let $\alpha_m$ and $\beta_n$ be two sequences of real numbers supported on $[M, 2M]$ and $[N, 2N]$ with $M = X^{1/2 - \delta}$ and $N = X^{1/2 + \delta}$. We show that there exists a $\delta_0 > 0$ such that the multiplicative convolution of $\alpha_m$ and $\beta_n$ has exponent of distribution $\frac{1}{2} + \delta-\varepsilon$ (in a weak sense) as long as $0 \leq \delta < \delta_0$, the sequence $\beta_n$ is Siegel-Walfisz and both sequences $\alpha_m$ and $\beta_n$ are bounded above by divisor functions. Our result is thus a general dispersion estimate for “narrow” type-II sums. The proof relies crucially on Linnik's dispersion method and recent bounds for trilinear forms in Kloosterman fractions due to Bettin-Chandee. We highlight an application related to the Titchmarsh divisor problem.
Keywords: equidistribution in arithmetic progressions, dispersion method.
Received: 22.06.2018
Accepted: 10.10.2018
Bibliographic databases:
Document Type: Article
UDC: 512.54
Language: English
Citation: Étienne Fouvry, Maksym Radziwiłł, “Another application of Linnik dispersion method”, Chebyshevskii Sb., 19:3 (2018), 148–163
Citation in format AMSBIB
\Bibitem{FouRad18}
\by \'Etienne~Fouvry, Maksym~Radziwi\l \l
\paper Another application of Linnik dispersion method
\jour Chebyshevskii Sb.
\yr 2018
\vol 19
\issue 3
\pages 148--163
\mathnet{http://mi.mathnet.ru/cheb685}
\crossref{https://doi.org/10.22405/2226-8383-2018-19-3-148-163}
\elib{https://elibrary.ru/item.asp?id=39454394}
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  • This publication is cited in the following 1 articles:
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    Full-text PDF :47
    References:23
     
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