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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2602.14845 |
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| _version_ | 1866910023872937984 |
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| author | Hammonds, Trajan |
| author_facet | Hammonds, Trajan |
| contents | The asymptotics of relative characters for real Lie groups were studied for representations $(π, σ)$ arising from Gan-Gross-Prasad pairs $(G,H)$ by Nelson and Venkatesh. They successfully compute the asymptotics of relative characters whenever the conductor of the associated Rankin-Selberg $L$-function $L(π\boxtimes σ^\vee)$ lies in a stable locus, i.e. away from conductor dropping. In this paper, we express asymptotics for relative characters in the non-archimedean setting for $(\mathrm{PGL}_2, \mathrm{GL}_1)$. The key new innovation is that our method overcomes the stability hypothesis and allows for significant conductor dropping. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14845 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Relative Character Asymptotics Beyond Stability for $\mathrm{PGL}_2 \times \mathrm{GL}_1$ Hammonds, Trajan Representation Theory Number Theory The asymptotics of relative characters for real Lie groups were studied for representations $(π, σ)$ arising from Gan-Gross-Prasad pairs $(G,H)$ by Nelson and Venkatesh. They successfully compute the asymptotics of relative characters whenever the conductor of the associated Rankin-Selberg $L$-function $L(π\boxtimes σ^\vee)$ lies in a stable locus, i.e. away from conductor dropping. In this paper, we express asymptotics for relative characters in the non-archimedean setting for $(\mathrm{PGL}_2, \mathrm{GL}_1)$. The key new innovation is that our method overcomes the stability hypothesis and allows for significant conductor dropping. |
| title | Relative Character Asymptotics Beyond Stability for $\mathrm{PGL}_2 \times \mathrm{GL}_1$ |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2602.14845 |