6 papers · 1 filter
The complexity of Ford domains of
Pengcheng Zhang
We investigate a particular choice of the Ford fundamental domain of the congruence subgroup and define a notion of complexity accordingly, which is a nonnegative…
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 -adic behaviors of meromorphic modular forms under the oper…
Ordinary primes for -type abelian varieties and weight modular forms
Tian Wang, Pengcheng Zhang
Let be a -dimensional abelian variety defined over a number field . It is conjectured that the set of ordinary primes of over has positive density, and this is kn…
A note on the hypergeometric datum and symmetric squares of elliptic curves
Pengcheng Zhang
This is an expository note on a mod congruence relating the truncated hypergeometric sums associated to to symmetric squ…
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 . The first result recovers a Hilbert modular form (of some level) from…
The 2-complexity of even positive integers
Pengcheng Zhang
The question of integer complexity asks about the minimal number of 's that are needed to express a positive integer using only addition and multiplication (and parentheses). In…