Author

Zhi-Xu Hua

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Preprint Aug 2026

Gevrey localization for simple and distinct zeros in a prime-modulus Dirichlet family

Let $q$ tend to infinity through odd primes, let $T=T(q)$, and put $\ell=\log(qT/2\pi)$. Suppose that $\ell^s=o(T)$ for some fixed $s>1$ and that \[ \lambda_{\rm bw}:=\min\left\{1, \liminf_{\substack{q\to\infty\\q\ \mathrm{prime}}} \frac{\log(q-1)}{\ell}\right\}>0. \] For the unweighted family of the $q-2$ nonprincipal...

Zhi-Xu Hua, Xiu-Fan Yang · 0 citations

Preprint Aug 2026

Simple and distinct zeros in a prime-modulus Dirichlet family from near-microscopic to polylogarithmic heights

Fix $\eta>0$ and $A_0>0$. Let $q$ tend to infinity through odd primes, put $Q=\log q$, and let $T=T(q)$ satisfy \[ \frac{(\log Q)^{1+\eta}}{Q}\le T\le Q^{A_0}. \] Set $I=(T,2T]$, and sum without weights over the $q-2$ nonprincipal characters modulo $q$. Let $\mathcal N_q$ count nontrivial zeros in \(I...

Zhi-Xu Hua, Xiu-Fan Yang · 0 citations