scholarly journals Higher power moments of the Riesz mean error term of symmetric square L-function

2011 ◽  
Vol 131 (12) ◽  
pp. 2247-2261 ◽  
Author(s):  
Kui Liu ◽  
Haiyan Wang
Keyword(s):  
Error Term ◽  
Mean Error ◽  
Riesz Mean ◽  
Higher Power ◽  
Symmetric Square ◽  
Power Moments

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

EULER–HADAMARD PRODUCTS AND POWER MOMENTS OF SYMMETRIC SQUARE L-FUNCTIONS

2013 ◽  
Vol 09 (03) ◽  
pp. 621-639 ◽  
Author(s):  
GORAN DJANKOVIĆ
Keyword(s):  
Modular Forms ◽  
Matrix Theory ◽  
Asymptotic Formulas ◽  
Hadamard Products ◽  
Central Value ◽  
General Power ◽  
Symmetric Square ◽  
Power Moments ◽  
Holomorphic Modular Forms ◽  
Work Done

In this paper we prove asymptotic formulas for general moments of partial Euler products and the first and the second moments of partial Hadamard products related to central values of the family of L-functions associated to the symmetric square lifts of holomorphic modular forms for SL2(ℤ). Then using a hybrid Euler–Hadamard product formula for the central value, we relate these results with conjectures for general power moments of L-functions in this family and with Random Matrix Theory interpretations. This continues the work done previously by Gonek–Hughes–Keating and Bui–Keating for other families of L-functions.

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