Z. Qi

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20232026

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8 papers · 1 filter

math.NT2026

Luo's Spectral Large Sieve Inequality on Short Intervals

Zhi Qi, Ruihua Qiao

Let $u_{j}$ traverse an orthonormal basis of Hecke--Maass forms for $SL_{2} (Z)$ with Hecke eigenvalues $λ_{j} (n)$ and Laplace eigenvalue $1/4 + t_{j}^{2}$ . In this paper…

math.NT2026

Mean Lindelöf Hypothesis and Prime Geodesic Theorem on Bianchi Manifolds

Changlin Li, Zhi Qi

In this paper, we prove the mean Lindelöf hypothesis for the second moment of symmetric square $L$ -functions and thereby obtain the (unconditional) error bound $O (x^{36/23+\vareps…

math.NT2026

On the Second Moment of $L (1/2, As (f) \times ϕ)$

Changlin Li, Zhi Qi

Let $F = Q (D)$ be a real quadratic field. In this paper, we establish a large sieve inequality for the Asai lifts $As (f)$ with $f$ in a Hecke or…

math.NT2025

The Second Moment of $GL_{4} \times GL_{2}$ $L$ -functions at Special Points

Zhi Qi, Ruihua Qiao

In this paper, we provide an alternative proof of Chandee and Li's result on the second moment of $GL_{4} \times GL_{2}$ special $L$ -values. Our method is conceptuall…

math.NT2024

On the Twisted Spectral Large Sieve Inequality for $PGL_{2} (Z [i]) \ PGL_{2} (C)$

Zhi Qi

In this paper, we extend the twisted spectral large sieve inequalities of Deshouillers, Iwaniec, Luo, and Young from $SL_{2} (Z)$ onto $\mathrm{PGL}_2 (\mathbb{Z}[i…

math.NT2024

Symmetric Square Large Sieve for $PSL_{2} (Z [i]) \ PSL_{2} (C)$ and Prime Geodesic Theorem for $PSL_{2} (Z [i]) \ H^{3}$

Zhi Qi

In this paper, we improve the error term in the prime geodesic theorem for the Picard manifold $PSL_{2} (Z [i]) \ H^{3}$ . Instead of $ \mathrm{P…

Luo's Spectral Large Sieve Inequality on Short Intervals

Mean Lindelöf Hypothesis and Prime Geodesic Theorem on Bianchi Manifolds

On the Second Moment of L(1/2,As(f)×ϕ)

The Second Moment of GL4​×GL2​ L-functions at Special Points

On the Twisted Spectral Large Sieve Inequality for PGL2​(Z[i])\PGL2​(C)

Symmetric Square Large Sieve for PSL2​(Z[i])\PSL2​(C) and Prime Geodesic Theorem for PSL2​(Z[i])\H3

On the Second Moment of $L (1/2, As (f) \times ϕ)$

The Second Moment of $GL_{4} \times GL_{2}$ $L$ -functions at Special Points

On the Twisted Spectral Large Sieve Inequality for $PGL_{2} (Z [i]) \ PGL_{2} (C)$

Symmetric Square Large Sieve for $PSL_{2} (Z [i]) \ PSL_{2} (C)$ and Prime Geodesic Theorem for $PSL_{2} (Z [i]) \ H^{3}$