arXiv subjects

Zeping Hao

Publications and source records attributed to Zeping Hao.

3 recordsLinked to original sources

arXiv2026

Algebraic functional equation for big Galois representations over multiple $\mathbb{Z}_p$-extensions

We present a general approach to establish algebraic functional equations for big Galois representations over multiple $\mathbb{Z}_p$-extensions. Our result is formulated in both Selmer group and Selmer complex settings, and encompasses a broad range of Iwasawa-theoretic scenarios. In particular, our result applies to the triple product of Hida families in both balanced and unbalanced cases, as well as the half-ordinary Rankin-Selberg universal deformations recently studied by the first named author and Loeffler. Our result also significantly generalizes many previously known cases of algebraic functional equations and answers a question of Greenberg.

math.NT↗

arXiv2025

Explicit Hecke eigenform product identities for Hilbert modular forms

Let $F$ be a totally real number field, and $g,f,h$ be Hilbert modular forms over $F$ that are Hecke eigenforms satisfying $g=f\cdot h$. We characterize such product identities among all real quadratic fields of narrow class number one, proving they occur only for $F=\mathbb Q(\sqrt{5})$, with precisely two such identities. We also shed some light on the general totally real case by showing that no such identity exists when both $f$ and $h$ are Eisenstein series of distinct weights.

math.NT↗

arXiv2024

P-adic Rankin-Selberg L-functions in universal deformation families and functional equations

We construct a $p$-adic Rankin-Selberg $L$-function associated to the product of two families of modular forms, where the first is an ordinary (Hida) family, and the second an arbitrary universal-deformation family (without any ordinarity condition at $p$). This gives a function on a 4-dimensional base space - strictly larger than the ordinary eigenvariety, which is 3-dimensional in this case. We prove our $p$-adic $L$-function interpolates all critical values of the Rankin-Selberg $L$-functions for the classical specialisations of our family, and derive a functional equation for our $p$-adic $L$-function.

math.NT↗