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arXiv · 2608.00807

Cycles for Rankin-Selberg $L$-functions, I: automorphic periods

Atsushi Ichino·Kartik Prasanna
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Abstract

In this paper, we establish an explicit formula for automorphic periods which will be used in a sequel to study special values of $p$-adic Rankin-Selberg $L$-functions. Our motivation is to extend the Bertolini-Darmon-Prasanna formula to the case where the archimedean local sign is opposite to that in the original setting. To this end, we prove a formula for the $\mathrm{GU}(1,1)$-period of a theta lift from $\mathrm{GSO}(2)$ to $\mathrm{GSp}_4$, which is adapted to $p$-adic interpolation. We also introduce a $p$-depletion Hecke operator for this theta lift, which will play a crucial role in relating the automorphic period to the image of the $p$-adic Abel-Jacobi map.

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Atsushi Ichino, Kartik Prasanna. 2026-08-01. Cycles for Rankin-Selberg $L$-functions, I: automorphic periods. https://arxiv.org/abs/2608.00807

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