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Author ORCID Identifier

https://orcid.org/0000-0002-8753-1132

AccessType

Open Access Dissertation

Document Type

dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mathematics

Year Degree Awarded

2022

Month Degree Awarded

May

First Advisor

Tom Weston

Subject Categories

Number Theory

Abstract

We extend known results on the behavior of Iwasawa invariants attached to Mazur-Tate elements for p-nonordinary modular forms of weight k=2 to higher weight modular forms with a_p=0. This is done by using a decomposition of the p-adic L-function due to R. Pollack in order to construct explicit lifts of Mazur-Tate elements to the full Iwasawa algebra. We then study the behavior of Iwasawa invariants upon projection to finite layers, allowing us to express the invariants of Mazur-Tate elements in terms of those coming from plus/minus p-adic L-functions. Our results combine with work of Pollack and Weston to relate the plus/minus and sharp/flat Iwasawa invariants attached to congruent pairs of modular forms at weights p+1 and 2, respectively.

DOI

https://doi.org/10.7275/28622575

Included in

Number Theory Commons

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