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

TL;DR

This paper investigates the Iwasawa invariants of Mazur-Tate elements associated with non-ordinary modular forms of higher Serre weight, providing asymptotic formulas and generalizations of known results.

Contribution

It introduces asymptotic formulas for Iwasawa invariants of Mazur-Tate elements for higher weight forms and extends previous Serre weight 2 results to larger weights.

Findings

Derived asymptotic formulas for Iwasawa invariants.

Connected invariants of Mazur-Tate elements with signed p-adic L-functions.

Generalized results to higher Serre weights beyond weight 2.

Abstract

Fix an odd prime $p$ and let $f$ be a non-ordinary eigen-cuspform of weight $k$ and level coprime to $p$. Assuming $p>k-1$, we compute asymptotic formulas for the Iwasawa invariants of the Mazur-Tate elements attached to $f$ in terms of the corresponding invariants of the signed $p$-adic $L$-functions. By combining this with a version of mod $p$ multiplicity one, we also obtain descriptions of the $\lambda$-invariants of Mazur-Tate elements attached to certain higher weight modular forms with Serre weight $<p+1$, generalizing results of Pollack and Weston in the Serre weight 2 case.