Show simple item record

dc.contributorRotger Cerdà, Víctor
dc.contributor.authorFernández Peña, Oriol
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.description.abstractThis master s thesis is intended to give a presentation of the theory of congruences between the Fourier coecients of modular forms. In order to do that we introduce the reader to the basic theory of modular forms from the beginning and we study the structure of their Fourier coecients in di↵erent ways using Hecke operators. Then we start the theory of congruences finding some of them by classical methods of Number Theory. After that, we introduce the advances made by Swinnerton-Dyer in the study of congruences using l-adic representations and the generalisation by Ken Ono. Finally, we explain the papers by Hida and Ribet in two chapters giving some conditions for the existence of congruences using the associated L-functions and decomposing the space of modular forms.
dc.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
dc.subject.lcshAutomorphic forms
dc.subject.lcshDiscontinuous groups
dc.subject.otherNumber Theory
dc.subject.otherModular Forms
dc.subject.otherCongruences between modular forms
dc.titleCongruences between modular forms
dc.typeMaster thesis
dc.subject.lemacFormes automòrfiques
dc.subject.lemacGrups discontinus
dc.subject.amsClassificació AMS::11 Number theory::11F Discontinuous groups and automorphic forms
dc.rights.accessOpen Access
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística

Files in this item


This item appears in the following Collection(s)

Show simple item record

Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain