Hui-Min Zheng

collaborators

6 papers

math.NT2026

A two-step supercongruence for an Apéry-like sequence

Huimin Zheng

Let $G_{n} = \sum_{k = 0}^{n} 4^{k} (n - k 2 n - 2 k)^{2} (k 2 k)$ . Zhi-Hong Sun conjectured that, for primes $p \equiv 3 (mod 4)$ , positive odd integers $m$ , and $r \geq 2$ , the two-step congr…

math.NT2026

A certified continuation machine for Mahler measure identities at CM points, with twelve new proofs of conjectures of Samart

Huimin Zheng

We axiomatize the differential-comparison continuation method of [Zf] into a general machine for proving Mahler measure identities at CM points: a modular parametrization with rigo…

math.NT2026

Boyd's conductor-11 Mahler measure conjecture: proof of the split-integral identity (C3), with an exact structural analysis of the family S_k

Huimin Zheng

Boyd's 1998 tables of conjectural identities $m (P) = r ∣ L^{'} (E, 0) ∣$ between Mahler measures of two-variable polynomials and $L$ -values of elliptic curves begin with the smallest possi…

math.NT2026

Samart's conjecture n_4(81)=40M_7: the exact CM evaluation and the two obstructions. A status report

Huimin Zheng

This note archives the status of Samart's Table-6 conjecture $n_{4} (81) = 40 M_{7}$ , $M_{7} := L^{'} (g_{7}, 0)$ , where $g_{7} (τ) = η (τ)^{3} η (7 τ)^{3}$ is the newform of $S_{3} (Γ_{0} (7), χ_{- 7})$ and $n_4(s):=4m(…

math.NT2026

Mahler measures at interior CM points: proofs of two conjectures of Samart

Huimin Zheng

We prove two conjectures of Samart as identities of genuine Mahler measures. The first is the case $k = 1$ of his evaluations for the family $(x + x^{- 1}) (y + y^{- 1}) (z + z^{- 1}) + k^{1/2}$ :…

math.NT2023

Pseudorandomness of Sato-Tate Distributions for Elliptic Curves

Chung Pang Mok, Huimin Zheng

In this paper we propose conjectures that assert that, the sequence of Frobenius angles of a given elliptic curve over $Q$ without complex multiplication is pseudorandom,…