p-adic L-functions for \mathrm U(2,1)×\mathrm U(1,1)

2025/11/24 by Harris, Michael, Hsieh, Ming-Lun, Yamana, Shunsuke
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2511.19552

Abstract

We construct the five-variable p-adic L-function attached to Hida families on \mathrm U(2,1)×\mathrm U(1,1), interpolating the square-root of Rankin-Selberg L-values in the shifted piano range. Our construction relies on a new theta operator and its p-adic variation which plays a role analogous to the classical Ramanujan-Serre theta operator in Hida's p-adic Rankin-Selberg method. The interpolation formula, including the modified Euler factors at p and at the real place, is consistent with the conjectural shape of p-adic L-functions predicted by Coates and Perrin-Riou.

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