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arXiv · 1312.0553

Shifted convolution sums and Burgess type subconvexity over number fields

P. Maga
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Abstract

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

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P. Maga. 2013-12-02. Shifted convolution sums and Burgess type subconvexity over number fields. https://arxiv.org/abs/1312.0553

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