Author

Rui-Chen Xu

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Preprint Oct 2026

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

Let $F$ be a number field and $f$ a normalized cuspidal Hecke eigenform on $\mathrm{GL}(2)$ over $F$, with $k/2$ as the central critical point of its $L$-function $L(f,s)$. Let $\mathfrak{p}$ be a totally split prime ideal of $F$ lying above an odd prime $p$ and coprime to the level ideal of $f$. In this article, we sh...

Rui-Chen Xu · 0 citations

Preprint Sep 2026

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

Let $p\geq 5$ be a prime, and let $f$ be a $p$-ordinary cuspidal newform of even weight $k = 2r \geq 2$ and level $N$, with $p \nmid N$ and trivial nebentype. In this article, we prove Kato's Iwasawa main conjecture for $f$, formulated in terms of the $p$-adic $L$-function of $f$, under the sole assumptions that the as...

Rui-Chen Xu · 0 citations