Number Theory Seminar

I will report joint work with D. Casazza and R. Sakamoto, where we formulate a conjecture (and prove it in many cases) on the factorization of a certain triple product p-adic L-function whose range of interpolation is empty. The relevant factorization statement reflects not only the Artin formalism for the underlying family of motives (which decompose as the sum of 2 motives of respective degrees 2 and 6) but also dwell on the interplay between various Gross--Zagier formulae for the relevant complex L-series, and the subtle relationship between the derivatives of complex L-series at their central critical point and p-adic L-functions.