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.

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