4 variable triple product p-adic L-functions

After Harris-Tilouine constructed one variable p-adic triple product L-functions, Darmon-Rotger constructed
three-variable p-adic triple product L-functions for three Hida families of elliptic newforms, using Ichino’s formula.
It interpolates central critical L-values, and outside the region of interpolation its special values are related to the image
of Gross-Schoen cycles under the p-adic Abel-Jacobi map.
This construction was refined by Greenberg-Seveso, Ming-Lun Hsieh and Isao Ishikawa.
In this talk I will add cyclotomic variable and construct four-variable p-adic triple product L-functions, which interpolate
all critical L-values in the balanced case, using Garret’s integral representation.
This refines the construction of the cyclotomic p-adic triple product L-functions by Boecherer-Panchishkin.
This is a joint work with Ming-Lun Hsieh.