Date of Submission
Spring 2015
Academic Programs and Concentrations
Mathematics
Project Advisor 1
John Cullinan
Abstract/Artist's Statement
It has recently been shown that a rational specialization of Jacobi polynomials, when reduced modulo a prime number p, has roots which coincide with the supersingular j- invariants of elliptic curves in characteristic p. These supersingular lifts are conjectured to be irreducible with maximal Galois groups. Using the theory of p-adic Newton Polygons, we provide a new infinite class of irreducibility and, assuming a conjecture of Hardy and Littlewood, give strong evidence for their Galois groups being as large as possible.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Recommended Citation
Gajek-Leonard, Rylan Jacob, "Irreducibility and Galois Properties of Lifts of Supersingular Polynomials" (2015). Senior Projects Spring 2015. 143.
https://digitalcommons.bard.edu/senproj_s2015/143
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