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On exceptional zeros of p-adic L-functions

Hold Date 2019-10-18 16:00~2019-10-18 17:00

Place Lecture Room M W1-C-513, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Shunsuke YAMANA (Osaka City University)

p-adic L-functions involve modified p-factors which measure the discrepancy between the p-adic and classical special values in the interpolation formula. It is a puzzling fact that this factor can vanish at the central point. Then the p-adic L-function trivially vanish at the point, and such a zero is called an exceptional zero. The p-adic L-function of an elliptic curve E has an exceptional zero if and only if E has split multiplicative reduction at p. The precise relation between derivative of the p-adic L-function and the algebraic part of the central value was conjectured by Mazur-Tate-Teitelbaum and proved by Greenberg-Stevens. In this talk I will determine the exceptional zeros of cyclotomic p-adic L-functions associated to three ordinary elliptic curves and prove an identity between double or triple derivatives of the p-adic L-function and central L-values.
This is a joint work with Ming-Lun Hsieh.