Higher Congruences Between Modular Forms

dc.contributor.advisor	Eischen, Ellen
dc.contributor.author	Hsu, Catherine
dc.date.accessioned	2018-09-06T21:56:16Z
dc.date.available	2018-09-06T21:56:16Z
dc.date.issued	2018-09-06
dc.description.abstract	In his seminal work on modular curves and the Eisenstein ideal, Mazur studied the existence of congruences between certain Eisenstein series and newforms, proving that Eisenstein ideals associated to weight 2 cusp forms of prime level are locally principal. In this dissertation, we re-examine Eisenstein congruences, incorporating a notion of “depth of congruence,” in order to understand the local structure of Eisenstein ideals associated to weight 2 cusp forms of squarefree level N. Specifically, we use a commutative algebra result of Berger, Klosin, and Kramer to bound the depth of mod p Eisenstein congruences (from below) by the p-adic valuation of φ(N). We then show how this depth of congruence controls the local principality of the associated Eisenstein ideal.	en_US
dc.identifier.uri	https://hdl.handle.net/1794/23742
dc.language.iso	en_US
dc.publisher	University of Oregon
dc.rights	All Rights Reserved.
dc.subject	Algebraic number theory	en_US
dc.subject	Congruences	en_US
dc.subject	Modular forms	en_US
dc.title	Higher Congruences Between Modular Forms
dc.type	Electronic Thesis or Dissertation
thesis.degree.discipline	Department of Mathematics
thesis.degree.grantor	University of Oregon
thesis.degree.level	doctoral
thesis.degree.name	Ph.D.

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