Equations over finite fields: Zeta function and Weil conjectures
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Date
2022-11-24Les auteurs
Neira Lopez, SantiagoDirecteur
Ochoa Arango, Jesus AlonsoÉditeur
Pontificia Universidad Javeriana
Faculté
Facultad de Ciencias
Programme
Matemáticas
Titre obtenu
Matemático (a)
Type
Tesis/Trabajo de grado - Monografía - Pregrado
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Titre anglais
Equations over finite fields: Zeta function and Weil conjecturesrésumé
This work is a review of the congruent zeta function and the Weil conjectures for non-singular
curves. We derive an equation to obtain the number of solutions of equations over finite fields
using Jacobi sums in order to compute the Zeta function for specific equations. Also, we
introduce the necessary algebraic concepts to prove the rationality and functionality of the zeta
function.
Abstrait
This work is a review of the congruent zeta function and the Weil conjectures for non-singular
curves. We derive an equation to obtain the number of solutions of equations over finite fields
using Jacobi sums in order to compute the Zeta function for specific equations. Also, we
introduce the necessary algebraic concepts to prove the rationality and functionality of the zeta
function.
Mots-clés
Weil ConjecturesCongruent Zeta function
Equations over finite fields
Gauss sum
Jacobi sum
Nonsingular Complete Curves
Divisors
Riemann-Roch Theorem
Keywords
Weil ConjecturesCongruent Zeta function
Equations over finite fields
Gauss sum
Jacobi sum
Nonsingular Complete Curves
Divisors
Riemann-Roch Theorem
Des thèmes
Matemáticas - Tesis y disertaciones académicasCampos finitos (Álgebra)
Ecuaciones
Procesos de Gauss
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