arXiv subjects
Publications and source records attributed to Zhengxiao Gao.
On imaginary quadratic fields, we establish the $\mathrm{GL}_2$ Bessel $δ$-method and prove the hybrid Weyl-type subconvexity bound for $\mathrm{GL}_2 \times \mathrm{GL}_1$ twisted $L$-functions in the Archimedean aspect of the Hecke character on $\mathrm{GL}_1$.
Let $g$ be a fixed holomorphic cusp form of arbitrary level and nebentypus. Let $χ$ be a primitive character of prime-power modulus $q = p^γ$. In this paper, we prove the following hybrid Weyl-type subconvexity bound \begin{align*} L (1/2 + it, g \otimes χ) \ll_{g, p, \varepsilon} ( (1+|t|) q )^{1/3+ \varepsilon} \end{align*} for any $\varepsilon > 0$.