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Rankin--Selberg integrals of opposite conductor--one newforms
Abstract
Let F be a nonarchimedean local field of characteristic zero and let n≥2. For r=n,n+1, let Πr be an irreducible tempered representation of GLr(F) of conductor one and with trivial central character. We evaluate the Rankin--Selberg integral of opposite newforms in Πn+1× Πn 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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BibTeX
@misc{liu2026rankinselberg,
title = {{Rankin--Selberg integrals of opposite conductor--one newforms}},
author = {Dongwen Liu and Lei Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11045},
eprint = {2609.11045},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11045},
}
RIS
TY - UNPB
TI - Rankin--Selberg integrals of opposite conductor--one newforms
AU - Dongwen Liu
AU - Lei Zhang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11045
UR - https://arxiv.org/abs/2609.11045
AB - Let F be a nonarchimedean local field of characteristic zero and let n≥2. For r=n,n+1, let Π_r be an irreducible tempered representation of GL_r(F) of conductor one and with trivial central character. We evaluate the Rankin--Selberg integral of opposite newforms in Π_n+1× Π_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.
ER -