论文标题
$ \ rm gl_3 \ times gl_2 $ $ $ $ $ l $ functions的曲折的界限与复合模量
A bound for twists of $\rm GL_3\times GL_2$ $L$-functions with composite modulus
论文作者
论文摘要
令$π$为$ \ rm sl_3（\ mathbf {z}）$的hecke-maass cusp表格，让$ g $为holomorphic或maass cusp form $ \ rm sl_2（\ mathbf {z}}）$。令$χ$为模量的原始dirichlet字符$ m = m_1m_2 $，$ m_i $ prime，$ i = 1,2 $。假设$ m^{1/2+2η} <m_1 <m^{1-2η} $，$ 0 <η<1/8 $。然后，我们有$$ l \ left（\ frac {1} {2}，π\ otimes g \ otimesχ\ right）\ ll_ {π，g，g，\ varepsilon} m^{3/2-+\ varepsilon}。 $$
Let $π$ be a Hecke-Maass cusp form for $\rm SL_3(\mathbf{Z})$ and let $g$ be a holomorphic or Maass cusp form for $\rm SL_2(\mathbf{Z})$. Let $χ$ be a primitive Dirichlet character of modulus $M=M_1M_2$ with $M_i$ prime, $i=1,2$. Suppose that $M^{1/2+2η}<M_1<M^{1-2η}$ with $0<η<1/8$. Then we have $$ L\left(\frac{1}{2},π\otimes g \otimes χ\right)\ll_{π,g,\varepsilon} M^{3/2-η+\varepsilon}. $$
