2024-06-15T21:14:53Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00008508
2023-01-16T03:54:06Z
697:698:699
On Riesz means of the coefficients of the Rankn--Selberg series
IVIC, ALEKSANDAR
MATSUMOTO, KOHJI
TANIGAWA, YOSHIO
open access
Cambridge University Press
We study Δ(x;φ), the error term in the asymptotic formula for Σ_n≤xc_n, where the c_ns are generated by the Rankin-Selberg series. Our main tools are Voronoї-type formulae. First we reduce the evaluation of Δ(x;φ) to that of Δ(x;φ), the error term of the weighted sum ∑_n≤_x(x-n)c_n. Then we prove an upper bound and a sharp mean square formula for Δ_1(x;φ), by applying the Voronoї formula of Meurman's type.We also prove that an improvement of the error term in the mean square formula would imply an improvement of the upper bound of Δ(x;φ). Some other related topics are also discussed.
Cambridge University Press
1999-07
eng
journal article
VoR
http://hdl.handle.net/2237/10255
https://nagoya.repo.nii.ac.jp/records/8508
0305-0041
Mathematical Proceedings of the Cambridge Philosophical Society
127
1
117
131
https://nagoya.repo.nii.ac.jp/record/8508/files/KOHJI_MATSUMOTO_On_rises_means_of_the_1999.pdf
application/pdf
359.0 kB
2018-02-19