Fouvry, Étienne and Radziwiłł, Maksym (2018) Another application of Linnik's dispersion method. Chebyshevskii Sbornik, 19 (3). pp. 148-163. ISSN 2226-8383. doi:10.22405/2226-8383-2018-19-3-148-163. https://resolver.caltech.edu/CaltechAUTHORS:20210825-184516487
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Abstract
Let be α_m and β_n---two sequences of real numbers supported on segments [M,2M] and [N,2N], where M = X^(1/2 − δ) and N = X^(1/2 + δ)... We prove the existence of such a constant δ₀ that the multiplicative convolution α_m and β_n has a distribution level 1/2 + δ - ε (in a weak sense), if only 0 ⩽ δ < δ₀, subsequence β_n is a Siegel-Walvis sequence, and both sequences α_m and β_n are bounded from above by the divisor function. Our result, therefore, is the overall variance estimate for "short", type II sums. The proof makes essential use of Linnik's dispersion method and recent estimates for trilinear sums with Kloosterman fractions due to Bettin and Chandy. We will also focus on the application of this result to the Titchmarsh divisor problem.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2018 Tula State Pedagogical University. Retrieved 06/22/2018; Accepted for publication 10/10/2018. | |||||||||
| Subject Keywords: | equidistribution in arithmetic progressions, dispersion method | |||||||||
| Issue or Number: | 3 | |||||||||
| Classification Code: | 2010 Mathematics Subject Classification. Primary 11N69 | |||||||||
| DOI: | 10.22405/2226-8383-2018-19-3-148-163 | |||||||||
| Record Number: | CaltechAUTHORS:20210825-184516487 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20210825-184516487 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 110518 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 26 Aug 2021 22:01 | |||||||||
| Last Modified: | 30 Aug 2021 22:54 |
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