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Title: Elliptic curves and a theorem of Gauss
Author: Karuk, Andriana
Director/Tutor: Soto Ballesteros, Eduard
Keywords: Corbes el·líptiques
Treballs de fi de grau
Nombres p-àdics
Sèries de Dirichlet
Funcions zeta
Elliptic curves
Bachelor's theses
p-adic numbers
Dirichlet series
Zeta functions
Issue Date: 18-Jan-2019
Abstract: [en] Just like in life, in mathematics many times we find ourselves seeking for the unknown as are the solutions of an equation. In our case instead of focusing on the solutions we would rather know how many options there are, and so how many solutions we can have in a given equation. The aim of this work is to study some of the properties of elliptic curves, as well as some additional theory related to the p-adic numbers and idèles. Moreover, we will see how a perfect combination of it all can helps to find out how many solutions there are of an elliptic curve over a finite field with some additional conditions.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Eduardo Soto Ballesteros
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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