Author

Zi-Kang Dong

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Preprint Aug 2026

Large zeta sums and zeros of the Riemann zeta function

For real $t$ and $x\ge 1$, set \[ S(x,t)=\sum_{n\le x} n^{\ii t}. \] We prove an unconditional inverse theorem relating large values of $S(x,t)$, with $|t|$ large, to zeros of the Riemann zeta function near height $t$. More precisely, if $T\le |t|\le 2T$, $\exp(\sqrt{\log T})\le x\le \sqrt T$, and $|S(x,t)|=x/N$ with $...

Zi-Kang Dong, Ruihua Wang, Weijia Wang et al. · 0 citations

Preprint Sep 2026

Extreme values of quadratic Hecke $L$-functions

We study large values of quadratic Hecke $L$-functions in the conductor aspect. Let $K$ be a fixed number field, and assume GRH for its finite-order Hecke $L$-functions. In a fixed ray class component with conductor norm comparable to $X$, we prove that \[ \max_\chi L\left(\frac12+\frac A{\log_2X},\chi\right) \geq\exp\...

Zi-Kang Dong, Long Liu · 1 citation · ⚡1