Ruihua Qiao | Searcharxiv

arXiv2026

Luo's Spectral Large Sieve Inequality on Short Intervals

Let $u_j $ traverse an orthonormal basis of Hecke--Maass forms for $\mathrm{SL}_2 (\mathbb {Z}) $ with Hecke eigenvalues $λ_j (n)$ and Laplace eigenvalue $1/4+t_j^2$. In this paper, we consider the short-interval variant of the twisted spectral large sieve inequality of Luo for $ λ_j (n) n^{it_j} $ on the range $t_j \leqslant T$ and prove that the `Eisenstein--Kloosterman' cancellation discovered by Luo is effective on the interval $ T < t_j \leqslant T + M $ as long as $\sqrt{T} < M \leqslant T$. Moreover, our approach yields an improvement of the large sieve inequality of Luo.

math.NT↗

arXiv2026

The Second Moment of $\mathrm{GL}_4 \times \mathrm{GL}_2$ $L$-functions at Special Points

In this paper, we provide an alternative proof of Chandee and Li's result on the second moment of $\mathrm{GL}_4 \times \mathrm{GL}_2$ special $L$-values. Our method is conceptually more direct as it neither detects the `Eisenstein--Kloosterman' cancellation nor uses the Poisson summation.

math.NT↗

arXiv2024

Meta-Learning-Based Fronthaul Compression for Cloud Radio Access Networks

This paper investigates the fronthaul compression problem in a user-centric cloud radio access network, in which single-antenna users are served by a central processor (CP) cooperatively via a cluster of remote radio heads (RRHs). To satisfy the fronthaul capacity constraint, this paper proposes a transform-compress-forward scheme, which consists of well-designed transformation matrices and uniform quantizers. The transformation matrices perform dimension reduction in the uplink and dimension expansion in the downlink. To reduce the communication overhead for designing the transformation matrices, this paper further proposes a deep learning framework to first learn a suboptimal transformation matrix at each RRH based on the local channel state information (CSI), and then to refine it iteratively. To facilitate the refinement process, we propose an efficient signaling scheme that only requires the transmission of low-dimensional effective CSI and its gradient between the CP and RRH, and further, a meta-learning based gated recurrent unit network to reduce the number of signaling transmission rounds. For the sum-rate maximization problem, simulation results show that the proposed two-stage neural network can perform close to the fully cooperative global CSI based benchmark with significantly reduced communication overhead for both the uplink and the downlink. Moreover, using the first stage alone can already outperform the existing local CSI based benchmark.

cs.IT↗