Pengcheng Zhang

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20242026

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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…

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

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

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