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arXiv · 2405.12611

P-adic Rankin-Selberg L-functions in universal deformation families and functional equations

Zeping Hao·David Loeffler
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Abstract

We construct a $p$-adic Rankin-Selberg $L$-function associated to the product of two families of modular forms, where the first is an ordinary (Hida) family, and the second an arbitrary universal-deformation family (without any ordinarity condition at $p$). This gives a function on a 4-dimensional base space - strictly larger than the ordinary eigenvariety, which is 3-dimensional in this case. We prove our $p$-adic $L$-function interpolates all critical values of the Rankin-Selberg $L$-functions for the classical specialisations of our family, and derive a functional equation for our $p$-adic $L$-function.

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Zeping Hao, David Loeffler. 2024-05-21. P-adic Rankin-Selberg L-functions in universal deformation families and functional equations. https://doi.org/10.1515/forum-2024-0497

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