Mathematics Seminar
Date: Wednesday, 8 January 2025
Time: 2:00 PM
Venue: Seminar Hall
Twisted triple product p-adic L-function for finite slope families and a p-adic Gross-Zagier formula
Ananyo Kazi
UniDistance Suisse.
08-01-25

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Abstract

In the theory of p-adic L-functions a p-adic Gross-Zagier formula gives interpretation to special values of p-adic L-functions outside the region of interpolation using p-adic integration. Seen as a first step towards "explicit reciprocity laws" they have important applications towards proving various instances of the Bloch-Kato conjecture, as in the work of Darmon–Rotger. We construct a p-adic twisted triple product L-function associated to finite slope families of Hilbert modular forms, assuming p unramified in the totally real fields. We use techniques of p-adic iteration of the Gauss–Manin connection on sheaves of nearly overconvergent modular forms, as developed by Andreatta–Iovita. In joint work with Ting-Han Huang, we prove a p-adic Gross-Zagier formula for this L-function for a pair of an elliptic modular form and a quadratic Hilbert modular form. This generalises work of Blanco-Chacon and Fornea for the case of Hida families, and we overcome a technical assumption in their work of p being split in the quadratic field.