Z. Qi

activity

20232026

collaborators

8 papers

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…

math.NT2024

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

Zhi Qi

In this paper, we introduce concise expressions for the complex Bessel integral that enables us to improve the spectral large sieve inequality of Watt for $\mathrm{PGL}_2 (\mathbb{…

math.NT2023

On the Hankel Transform of Bessel Functions on Complex Numbers and Explicit Spectral Formulae over the Gaussian Field

Zhi Qi

In this paper, on the complex field $C$ , we prove two integral formulae for the Hankel-Mellin transform and the double Fourier-Mellin transform of Bessel functions, both r…

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

On the Hankel Transform of Bessel Functions on Complex Numbers and Explicit Spectral Formulae over the Gaussian Field

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 $PSL_{2} (Z [i]) \ H^{3}$

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