Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two

Abstract: Fix an odd prime $p$ and let $f$ be a non-ordinary eigen-cuspform of weight $k$ and level coprime to $p$. In this talk, we describe asymptotic formulas for the Iwasawa invariants of the Mazur--Tate elements attached to $f$ of weight $k\leq p$ in terms of the corresponding invariants of the signed $p$-adic $L$-functions. Combined with a version of mod $p$ multiplicity one, we use these formulas to obtain descriptions of the $\lambda$-invariants of Mazur--Tate elements attached to certain higher weight modular forms having Serre weight $\leq p$, generalizing results of Pollack and Weston in the Serre weight 2 case. This is joint work with Antonio Lei.

number theory

Audience: researchers in the topic

Five College Number Theory Seminar