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arXiv · 2609.11045

Rankin--Selberg integrals of opposite conductor--one newforms

Dongwen Liu·Lei Zhang
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Abstract

Let $F$ be a nonarchimedean local field of characteristic zero and let $n\geq2$. For $r=n,n+1$, let $\Pi_r$ be an irreducible tempered representation of ${\rm GL}_r(F)$ of conductor one and with trivial central character. We evaluate the Rankin--Selberg integral of opposite newforms in $\Pi_{n+1}\times \Pi_n$ explicitly and show that its central value is nonzero. As an application, this implies a case of Disegni--Zhang's conjecture on the nonvanishing of local relative characters.

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BibTeXRIS

Dongwen Liu, Lei Zhang. 2026-09-10. Rankin--Selberg integrals of opposite conductor--one newforms. https://arxiv.org/abs/2609.11045

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