scholarly journals On the Rankin-Selberg problem: higher power moments of the Riesz mean error term

2008 ◽  
Vol 51 (1) ◽  
pp. 148-160 ◽  
Author(s):  
Yoshio Tanigawa ◽  
WenGuang Zhai ◽  
DeYu Zhang
Keyword(s):  
Error Term ◽  
Mean Error ◽  
Riesz Mean ◽  
Higher Power ◽  
Power Moments

scholarly journals Power Moments of the Riesz Mean Error Term of Symmetric Square L-Function in Short Intervals

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2036
Author(s):  
Rui Zhang ◽  
Xue Han ◽  
Deyu Zhang
Keyword(s):  
Error Term ◽  
Asymptotic Formulas ◽  
Short Intervals ◽  
Mean Error ◽  
Riesz Mean ◽  
Hecke Eigenform ◽  
Symmetric Square ◽  
Power Moments

Let f(z) be a holomorphic Hecke eigenform of weight k with respect to SL(2,Z) and let L(s,sym2f)=∑n=1∞cnn−s,ℜs>1 denote the symmetric square L-function of f. In this paper, we consider the Riesz mean of the form Dρ(x;sym2f)=L(0,sym2f)Γ(ρ+1)xρ+Δρ(x;sym2f) and derive the asymptotic formulas for ∫T−HT+HΔρk(x;sym2f)dx, when k≥3.

scholarly journals The third-power moment of the Riesz mean error term of symmetric square $ L $-function

2021 ◽  
Vol 6 (9) ◽  
pp. 9436-9445
Author(s):  
Rui Zhang ◽  
◽  
Xiaofei Yan
Keyword(s):  
Error Term ◽  
Power Moment ◽  
The Third ◽  
Mean Error ◽  
Riesz Mean ◽  
Symmetric Square

scholarly journals On the fourth power moment of the error term for the divisor problem with congruence conditions

2018 ◽  
Vol 14 (06) ◽  
pp. 1525-1546 ◽  
Author(s):  
Jinjiang Li ◽  
Min Zhang
Keyword(s):  
Asymptotic Formula ◽  
Error Term ◽  
Congruence Class ◽  
Divisor Problem ◽  
Fourth Power ◽  
Power Moment ◽  
Higher Power ◽  
Power Moments

Let [Formula: see text] denote the number of factorizations [Formula: see text], where each of the factors [Formula: see text] belongs to a prescribed congruence class [Formula: see text]. Let [Formula: see text] be the error term of the asymptotic formula of [Formula: see text]. In this paper, we establish an asymptotic formula of the fourth power moment of [Formula: see text] and prove that [Formula: see text] with [Formula: see text], which improves the previous value [Formula: see text] of Liu [On higher-power moments of the error term for the divisor problem with congruence conditions, Monatsh. Math. 163(2) (2011) 175–195].

On higher-power moments of $$\Delta_{(1)}(x)$$

2020 ◽  
Vol 162 (2) ◽  
pp. 445-464
Author(s):  
D. Liu ◽  
Y. Sui
Keyword(s):  
Higher Power ◽  
Power Moments

scholarly journals On higher-power moments of Δ(x) (III)

2005 ◽  
Vol 118 (3) ◽  
pp. 263-281 ◽  
Author(s):  
Wenguang Zhai
Keyword(s):  
Higher Power ◽  
Power Moments

scholarly journals On higher-power moments of E(t)

2004 ◽  
Vol 115 (4) ◽  
pp. 329-348 ◽  
Author(s):  
Wenguang Zhai
Keyword(s):  
Higher Power ◽  
Power Moments
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