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| Moments of L-Functions Attached to the Twist ofModular Form by Dirichlet Characters |
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Citation： |
Guanghua JI,Haiwei SUN.Moments of L-Functions Attached to the Twist ofModular Form by Dirichlet Characters[J].Chinese Annals of Mathematics B,2015,36(2):237~252 |
| Page view： 2107
Net amount： 1667 |
Authors： |
Guanghua JI; Haiwei SUN; |
Foundation： |
the National Natural Science Foundation of China (No. 11301299), the Natural
Science Foundation of Shandong Province (No. ZR2012AQ001) and the Specialized Research Fund
for the Doctoral Program of Higher Education (New Teachers) (Nos. 20110131120001, 20120131120075). |
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| Abstract： |
Let $f(z)$ be a holomorphic cusp form of weight $\kappa$ with respect to the full
modular group $SL_{2}(\mathbb{Z})$. Let $L(s,f)$ be the automorphic
$L$-function associated with $f(z)$ and $\chi$ be a Dirichlet
character modulo $q$. In this paper, the authors prove that
unconditionally for $k=\frac{1}{n}$ with $n\in \mathbb{N}$,
M_{k}(q,f)=\sum\limits_{{\chi({\rm mod}\,q)}\atop {\chi\neq\chi_0}
}\Big|L\Big(\frac{1}{2},f\otimes\chi\Big)\Big|^{2k}\ll_k\phi(q)(\log
q)^{k^2},
and the result also holds for any real number $00$ and any large prime $q$. |
Keywords： |
Moments, Automorphic L-functions, Convexity theorem |
Classification： |
11M41, 11F66, 11M06 |
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