Guitart Morales, XavierAlonso Aparcio, Joan Andreu2017-06-282017-06-282017-02-01https://hdl.handle.net/2445/112982Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Xavier Guitart Morales, 2017We construct the field of p-adic numbers as the completion of the rational numbers with respect to the p-adic distance. We also give the definition of the p-adic $\zeta$ function: a function of a p-adic variable that interpolates the values of Riemann’s $\zeta$ function at negative integers, and which we construct using the theory of p-adic integration.35 p.application/pdfcatcc-by-nc-nd (c) Joan Andreu Alonso Aparicio, 2017http://creativecommons.org/licenses/by-nc-nd/3.0/esNombres p-àdicsTreballs de fi de grauNombres racionalsFuncions zetap-adic numbersBachelor's thesesRational numbersZeta functionsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess