论文标题
Hecke $ l $ - 功能的第十二瞬间
The Twelfth Moment of Hecke $L$-Functions in the Weight Aspect
论文作者
论文摘要
我们证明了与HOLOMORTHIC HECKE CUSP相关的Hecke $ l $ unctions的第十二刻，重量$ k $在二元间隔$ t \ leq k \ leq k \ leq 2t $ as $ t $ at $ t $趋于无限。此结合恢复了Weyl-STRENT RENCTENTAMCONVEX BOND $ L（1/2，f）\ ll _ {\ varepsilon} k^{1/3 + \ varepsilon} $，并表明，对于任何$Δ> 0 $ $ o _ {\ varepsilon}（t^{12Δ+ \ varepsilon}）$ hecke cusp form $ f $ f $ of $ t $。我们的结果与Jutila相关的结果与Hecke-Maass cusp表格相关的Hecke $ L $ functions的第十二刻。该证明以关键方式使用了Kuznetsov的光谱互惠公式，该公式将由测试功能加权的$ L（1/2，f）的第四刻与由不同的测试功能加权的双重第四刻。
We prove an upper bound for the twelfth moment of Hecke $L$-functions associated to holomorphic Hecke cusp forms of weight $k$ in a dyadic interval $T \leq k \leq 2T$ as $T$ tends to infinity. This bound recovers the Weyl-strength subconvex bound $L(1/2,f) \ll_{\varepsilon} k^{1/3 + \varepsilon}$ and shows that for any $δ> 0$, the sub-Weyl subconvex bound $L(1/2,f) \ll k^{1/3 - δ}$ holds for all but $O_{\varepsilon}(T^{12δ+ \varepsilon})$ Hecke cusp forms $f$ of weight at most $T$. Our result parallels a related result of Jutila for the twelfth moment of Hecke $L$-functions associated to Hecke-Maass cusp forms. The proof uses in a crucial way a spectral reciprocity formula of Kuznetsov that relates the fourth moment of $L(1/2,f)$ weighted by a test function to a dual fourth moment weighted by a different test function.
