Rui-Chen Xu

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math.NT2026

Nonvanishing of special $L$ -values of cusp forms on $GL (2)$ with totally split prime power twists: without the class number hypothesis

Ruichen Xu

Let $F$ be a number field and $f$ a normalized cuspidal Hecke eigenform on $GL (2)$ over $F$ , with $k /2$ as the central critical point of its $L$ -function $L (f, s)$ . Let $\m…

math.NT2026

Zeta elements for $p$ -ordinary modular forms over imaginary quadratic fields and applications

Ruichen Xu

Let $p \geq 5$ be a prime, and let $f$ be a $p$ -ordinary cuspidal newform of even weight $k = 2 r \geq 2$ and level $N$ , with $p ∤ N$ and trivial nebentype. In this article, we p…

math.NT2026

Pseudonullity for fine Selmer groups over multiple $Z_{p}^{d}$ -extensions

Peikai Qi, Ruichen Xu

In this article, we develop vertical control theorems for fine Selmer groups associated with Galois representations and their deformations in $p$ -adic families. We apply them to pr…

Nonvanishing of special L-values of cusp forms on GL(2) with totally split prime power twists: without the class number hypothesis

Zeta elements for p-ordinary modular forms over imaginary quadratic fields and applications

Pseudonullity for fine Selmer groups over multiple Zpd​-extensions

Nonvanishing of special $L$ -values of cusp forms on $GL (2)$ with totally split prime power twists: without the class number hypothesis

Zeta elements for $p$ -ordinary modular forms over imaginary quadratic fields and applications

Pseudonullity for fine Selmer groups over multiple $Z_{p}^{d}$ -extensions