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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/10.7275/28631712
Recommended Citation
Gajek-Leonard, Rylan J., "On the Iwasawa Invariants of Nonordinary Modular Forms" (2022). Doctoral Dissertations. 2520.
https://doi.org/10.7275/28631712
https://scholarworks.umass.edu/dissertations_2/2520