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

We extend the construction of the p-adic L-function interpolating unitary Friedberg--Jacquet periods in arXiv: 2110. 05426 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 the results in arXiv: 2311. 14438. 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.