Zihao Liu

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math.NT2025

Explicit quadratic large sieve inequality

Zihao Liu

In this article, we obtain an explicit version of Heath-Brown's large sieve inequality for quadratic characters and discuss its applications to $L$ -functions and quadratic fields.

math.NT2023

On sums of Fourier coefficients of cusp forms twisted with additive characters

Zihao Liu

When $a_{n}$ is the $n$ 'th coefficient of some holomorphic cusp form, we prove a variety of Omega results for the twisted sum $\sum_{n \leq x} a_{n} e^{2 π in α}$ and discuss their applicatio…