2024-06-14T12:18:18Z
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2023-01-16T03:54:06Z
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On Riesz means of the coefficients of the Rankn--Selberg series
IVIC, ALEKSANDAR
23835
MATSUMOTO, KOHJI
23836
TANIGAWA, YOSHIO
23837
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.
journal article
Cambridge University Press
1999-07
application/pdf
Mathematical Proceedings of the Cambridge Philosophical Society
1
127
117
131
http://hdl.handle.net/2237/10255
0305-0041
https://nagoya.repo.nii.ac.jp/record/8508/files/KOHJI_MATSUMOTO_On_rises_means_of_the_1999.pdf
eng
Cambridge University Press