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memoria.pdf (510.48 KB)

Document type

Bachelor thesis

Publication date

2019-01-18

Publication license

cc-by-nc-nd (c) Andriana Karuk, 2018
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/140141

Elliptic curves and a theorem of Gauss

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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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Eduardo Soto Ballesteros

Subject

Corbes el·líptiques, Treballs de fi de grau, Nombres p-àdics, Sèries de Dirichlet, Funcions zeta

Subject (English)

Elliptic curves, Bachelor's theses, p-adic numbers, Dirichlet series, Zeta functions

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

KARUK, Andriana. Elliptic curves and a theorem of Gauss. [consulted: 11 of August of 2026]. Available at: https://hdl.handle.net/2445/140141

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