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Subconvexity for twisted L-functions over number fields via shifted convolution sums

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Abstract

Assume that \({\pi}\) is a cuspidal automorphic \({{\rm GL}_{2}}\) representation over a number field F. Then for any Hecke character \({\chi}\) of conductor \({\mathfrak{q}}\), the subconvex bound

$$L(1/2,\pi \otimes \chi) \ll_{F,\pi,\chi_{\infty},\varepsilon} \mathcal{N}{\mathfrak{q}}^{3/8+\theta/4+\varepsilon}$$

holds for any \({\varepsilon > 0}\), where \({\theta}\) is any constant towards the Ramanujan-Petersson conjecture (\({\theta = 7/64}\) is admissible). In these notes, we derive this bound from the spectral decomposition of shifted convolution sums worked out by the author in [21].

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  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, 1053, Budapest, Hungary

    P. Maga

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  1. P. Maga
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Maga, P. Subconvexity for twisted L-functions over number fields via shifted convolution sums. Acta Math. Hungar. 151, 232–257 (2017). https://doi.org/10.1007/s10474-016-0681-3

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