Relative Character Asymptotics Beyond Stability for $\PGL_2 \times \GL_1$

Abstract: The asymptotics of relative characters for real Lie groups were studied for representations $(\pi, \sigma)$ 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 $L(\pi \boxtimes \sigma^\vee)$ lies in a stable locus, i.e. away from conductor dropping. In this talk, we will show asymptotics for relative characters in the non-archimedean setting for $(\PGL_2, \GL_1)$. The key new innovation is that our method overcomes the stability hypothesis and allows for significant conductor dropping.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html