Si-Zhe Xie

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20232026

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math.NT2026

Prime pairs along rays of prime indices

Shenghao Hua, Sizhe Xie

Let $p_{j}$ be the prime with index $j$ . We prove that the ratios $m / n$ for which $p_{m} + p_{n}$ is a square are dense in $R_{> 0}$ . The same is true when $∣ p_{m} - p_{n} ∣$ is a square.…

math.NT2026

Multiple Gauss sums

Jianya Liu, Sizhe Xie

A multiple Gauss sum is a complete multiple exponential sum twisted by Dirichlet characters. We prove a new bound for multiple Gauss sums and, as an application, improve previous r…