Author

Hui-Min Zheng

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Preprint Oct 2026

Dihedral fields with Bloch lattice index five and quadratic subfield Q(i)

We construct infinitely many Galois extensions $M/\mathbb{Q}$ with dihedral group of order ten, quadratic subfield $\mathbb{Q}(i)$, and Bloch lattice index $Q_2(M)=5$. More precisely, we specify a Chebotarev set of rational primes of density $1/50$. For every prime $\ell$ in this set, at least two of four mixed cyclic...

Hui-Min Zheng · 0 citations

Preprint Sep 2026

A two-step supercongruence for an Ap\'ery-like sequence

Let $G_n=\sum_{k=0}^n4^k\binom{2n-2k}{n-k}^{2}\binom{2k}{k}$. Zhi-Hong Sun conjectured that, for primes $p\equiv3\pmod4$, positive odd integers $m$, and $r\ge2$, the two-step congruence $G_{(mp^r-1)/2}\equiv p^2G_{(mp^{r-2}-1)/2}\pmod {p^{2r-1}}$ holds. We prove the stronger valuation statement $G_{(p^2M-1)/2}-p^2G_{(M...

Hui-Min Zheng · 0 citations