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Understanding the factorization mod p of polynomials via modular forms

Author

Torrents Juste, Eloi

Other authors

Universitat Politècnica de Catalunya. Departament de Matemàtiques

Lario Loyo, Joan Carles

Masdeu, Marc

Publication date

2020-10

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Abstract

In this work we shall relate the factorization of polynomials modulo p with the splitting of primes in number fields, and we shall study in which cases the different possibilities of factorization or splitting can be explained by the coefficients of the q-expansion of a certain modular form.

Document Type

Master thesis

Language

English

Subjects and keywords

Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres; Number theory; Class field theory; Modular forms; Nombres, Teoria dels; Classificació AMS::11 Number theory

Publisher

Universitat Politècnica de Catalunya

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Rights

http://creativecommons.org/licenses/by-nc-sa/3.0/es/

Open Access

This item appears in the following Collection(s)

Treballs acadèmics [82541]