Pengcheng Zhang

collaborators

5 papers

math.NT2026

The complexity of Ford domains of $I^_{0} (N)$

Pengcheng Zhang

We investigate a particular choice of the Ford fundamental domain of the congruence subgroup $I^_{0} (N)$ and define a notion of complexity $c (N)$ accordingly, which is a nonnegative…

math.NT2026

Elliptic curves and Fourier coefficients of meromorphic modular forms

Pengcheng Zhang

We discuss several congruences satisfied by the coefficients of meromorphic modular forms, or equivalently, the $p$ -adic behaviors of meromorphic modular forms under the $U_{p}$ oper…

math.NT2026

Ordinary primes for $GL_{2}$ -type abelian varieties and weight $2$ modular forms

Tian Wang, Pengcheng Zhang

Let $A$ be a $g$ -dimensional abelian variety defined over a number field $F$ . It is conjectured that the set of ordinary primes of $A$ over $F$ has positive density, and this is kn…

math.NT2025

A note on the hypergeometric datum $((\frac{1}{2}, \frac{1}{6}, \frac{5}{6}), (1, 1))$ and symmetric squares of elliptic curves

Pengcheng Zhang

This is an expository note on a mod $p$ congruence relating the truncated hypergeometric sums associated to $((\frac{1}{2}, \frac{1}{6}, \frac{5}{6}), (1, 1))$ to symmetric squ…

math.NT2025

On converse theorems for Hilbert modular forms assuming unramified twists

Pengcheng Zhang

We prove two results on converse theorems for Hilbert modular forms over totally real fields of degree $r > 1$ . The first result recovers a Hilbert modular form (of some level) from…

The complexity of Ford domains of I^0​(N)

Elliptic curves and Fourier coefficients of meromorphic modular forms

Ordinary primes for GL2​-type abelian varieties and weight 2 modular forms

A note on the hypergeometric datum ((21​,61​,65​),(1,1)) and symmetric squares of elliptic curves

On converse theorems for Hilbert modular forms assuming unramified twists

The complexity of Ford domains of $I^_{0} (N)$

Ordinary primes for $GL_{2}$ -type abelian varieties and weight $2$ modular forms

A note on the hypergeometric datum $((\frac{1}{2}, \frac{1}{6}, \frac{5}{6}), (1, 1))$ and symmetric squares of elliptic curves