Iwasawa Invariants of Modular Forms with $a_p=0$

Abstract: Mazur-Tate elements provide a convenient method to study the analytic Iwasawa theory of $p$-nonordinary modular forms, where the associated $p$-adic $L$-functions have unbounded coefficients. The Iwasawa invariants of Mazur-Tate elements are well-understood in the case of weight 2 modular forms, where they can be related to the growth of $p$-Selmer groups and decompositions of the $p$-adic $L$-function. At higher weights, less is known. By constructing certain lifts to the full Iwasawa algebra, we compute the Iwasawa invariants of Mazur-Tate elements for higher weight modular forms with $a_p=0$ in terms of the plus/minus invariants of the $p$-adic $L$-function. Combined with results of Pollack-Weston, this forces a relation between the plus/minus invariants at weights 2 and $p+1$.

number theory

Audience: researchers in the topic

Algebra and Number Theory Seminars at Université Laval