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A $p$-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties
2015
Mathematics of Computation
Mazur, Tate, and Teitelbaum gave a p-adic analogue of the Birch and Swinnerton-Dyer conjecture for elliptic curves. We provide a generalization of their conjecture in the good ordinary case to higher dimensional modular abelian varieties over the rationals by constructing the p-adic L-function of a modular abelian variety and showing that it satisfies the appropriate interpolation property. This relies on a careful normalization of the p-adic L-function, which we achieve by a comparison of
doi:10.1090/mcom/3029
fatcat:7udy5hw2rvdytbjhug7p6of2qm