Anticyclotomic p-adic L-functions for Rankin--Selberg product

2023/06/12 by Liu, Yifeng
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2306.07039

Abstract

We construct p-adic L-functions for Rankin--Selberg products of automorphic forms of hermitian type in the anticyclotomic direction for both root numbers. When the root number is +1, the construction relies on global Bessel periods on definite unitary groups which, due to the recent advances on the global Gan--Gross--Prasad conjecture, interpolate classical central L-values. When the root number is -1, we construct an element in the Iwasawa Selmer group using the diagonal cycle on the product of unitary Shimura varieties, and conjecture that its p-adic height interpolates derivatives of cyclotomic p-adic L-functions. We also propose the nonvanishing conjecture and the main conjecture in both cases.

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• Anticyclotomic main conjecture and the non-triviality of Rankin-Selberg L-values in Hida families
• Iwasawa Main Conjecture for Rankin-Selberg p-adic L-functions: Non-Ordinary Case
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