Unitary Friedberg–Jacquet periods and anticyclotomic p-adic L-functions

Abstract We extend the construction of the p -adic L -function interpolating unitary Friedberg–Jacquet periods in previous work of the author to include the p -adic variation of Maass–Shimura differential operators. In particular, we develop a theory of nearly overconvergent automorphic forms in higher degrees of coherent cohomology for unitary Shimura varieties generalising previous work for modular curves. The construction of this p -adic L -function can be viewed as a higher-dimensional generalisation of the work of Bertolini–Darmon–Prasanna and Castella–Hsieh, and the inclusion of this extra variable arising from the p -adic iteration of differential operators will play a key role in relating values of this p -adic L -function to p -adic regulators of special cycles on unitary Shimura varieties.