Equations over finite fields: Zeta function and Weil conjectures
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Data
2022-11-24Autore
Neira Lopez, SantiagoDirettore
Ochoa Arango, Jesus AlonsoPublishers
Pontificia Universidad Javeriana
facoltà
Facultad de Ciencias
programma
Matemáticas
Titolo ottenuto
Matemático (a)
Tipo
Tesis/Trabajo de grado - Monografía - Pregrado
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Titolo inglese
Equations over finite fields: Zeta function and Weil conjecturesSommario
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.
Astratto
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.
Parole chiave
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
Tema
Matemáticas - Tesis y disertaciones académicasCampos finitos (Álgebra)
Ecuaciones
Procesos de Gauss
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