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.

Open Access Agreement

Open Access

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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Number Theory Commons

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