# Non-commutative q-expansions

##### Citations

4 citations

##### References

383 citations

### "Non-commutative q-expansions" refers background in this paper

...Introduction The theory of p-adic modular forms essentially began with the paper of Serre [15]....

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...The theory of p-adic modular forms essentially began with the paper of Serre [15]....

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360 citations

### "Non-commutative q-expansions" refers methods in this paper

...Since then they have formed a central tool in number theory and have most notably been used to prove main conjectures of commutative Iwasawa theory (Wiles [18], Skinner-Urban [17] etc....

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355 citations

### "Non-commutative q-expansions" refers methods in this paper

...Theorem 1 (Deligne-Ribet [4], theorem 6....

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...It was generalised by Katz [11] and Deligne-Ribet [4] and used to construct p-adic Lfunctions for CM and totally real number fields respectively....

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...Theorem 1 (Deligne-Ribet [4], theorem 6.1)....

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302 citations

### "Non-commutative q-expansions" refers background in this paper

...As F1 is an abelian extension of Q and G1 is pro-p we know by the theorem of Ferrero-Washington [5] that Ei ∈ A(G ab i ) × (it is enough to show that the constant term, i....

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...As F1 is an abelian extension of Q and G1 is pro-p we know by the theorem of Ferrero-Washington [5] that Ei ∈ A(G ab i ) × (it is enough to show that the constant term, i.e. the p-adic zeta functions ζ(Ki/Fi), of Ei are units in Λ(G ab i )S ....

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284 citations

### "Non-commutative q-expansions" refers methods in this paper

...It was generalised by Katz [11] and Deligne-Ribet [4] and used to construct p-adic Lfunctions for CM and totally real number fields respectively....

[...]