p-adic L-functions, p-adic Gross-Zagier formulas and plectic points
Víctor Hernández Barrios
Abstract:In this work we generalize the construction of p-adic anticyclotomic L-functions associated to an elliptic curve E/F and a quadratic extension K/F, by defining a measure µ_f^p attached to K/F and an automorphic
form. In the case of parallel 2, the automorphic form is associated with an elliptic curve E/F.
The first main result is a p-adic Gross-Zagier formula: if E has split multiplicative reduction at p and p does not split at K/F, we compute the first derivative of the p-adic L-function by relati… Show more
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