Shifted convolution sums and Burgess type subconvexity over number fields

Abstract

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

References in corpus (2)

• The subconvexity problem for $\GL_{2}$
• Burgess-like subconvex bounds for $G{L}_2\times G{L}_1$

Cited by in corpus (2)

• Subconvexity for sup-norms of automorphic forms on PGL(n)
• Twisted Hilbert modular L-functions and spectral theory