Title: Exceptional zero formulas for anticyclotomic p-adic L-functions
Abstract: In this note we define anticyclotomic p-adic measures attached to a finite set of places S above p, a modular elliptic curve E over a general number field F and a quadratic extension K/F. We study the exceptional zero phenomenon that arises when E has multiplicative reduction at some place in S. In this direction, we obtain p-adic Gross-Zagier formulas relating derivatives of the corresponding p-adic L-functions to the extended Mordell-Weil group E(K). We describe first the case S={P} depicting the leading coefficient of the anticyclotomic p-adic L-function in terms of Darmon points. Our final result generalizes a recent result which uses the construction of plectic points due to Fornea and Gehrmann. We obtain a general formula for arbitrary S that computes the r-th derivative of the p-adic L-function, where r is the number of places in S where E has multiplicative reduction, in terms of plectic points and Tate periods of E.
Publication Year: 2021
Publication Date: 2021-07-05
Language: en
Type: preprint
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