Shifted convolution sums and Burgess type subconvexity over number fields

Let $F$ be a number field and $\pi$ an irreducible cuspidal representation of ${\mathrm{G}\mathrm{L}}_2(F)\mathrm{\backslash }{\mathrm{G}\mathrm{L}}_2(\mathbf{A})$ with unitary central character. Then the bound $$L(1\mathrm{/}2,\pi \otimes \chi ){\ll }_{F,\pi ,{\chi }_{\mathrm{\infty }},\epsilon }\mathcal{N}(\mathfrak{q}{)}^{3\mathrm{/}8+\theta \mathrm{/}4+\epsilon }$$ holds for any Hecke character $\chi$ of conductor $\mathfrak{q}$, where $\theta$ is any constant towards the Ramanujan-Petersson conjecture ($\theta =7\mathrm{/}64$ is admissible). The proof is based on a spectral decomposition of shifted convolution sums.