Pengcheng Zhang

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20242026

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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…

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

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