Higher Congruences Between Modular Forms

@article{Katz1975HigherCB,
  title={Higher Congruences Between Modular Forms},
  author={Nicholas M. Katz},
  journal={Annals of Mathematics},
  year={1975},
  volume={101},
  pages={332}
}
  • N. Katz
  • Published 1 March 1975
  • Mathematics
  • Annals of Mathematics
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83 Citations
Highly Influential Citations
5
Background Citations
13
Methods Citations
6
Results Citations
3

83 Citations

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Citation Type

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. In this paper we prove that there are finitely many modular curves that admit a smooth plane model. Moreover, if the degree of the model is greater than or equal to 10 , no such curve exists. For…
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We show that the completed Hecke algebra of $p$-adic modular forms is isomorphic to the completed Hecke algebra of continuous $p$-adic automorphic forms for the units of the quaternion algebra…
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In this article, we first give a complete description of the algebra of integer weight modular forms on the congruence subgroup $$\Gamma _0(2)$$ modulo a prime $$p\ge 3$$ . This result parallels…
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Perfectoid geometry of p-adic modular forms
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References

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Soient K un corps de nombres algebriques totalement reel, et ζK sa fonction zeta. D’apres un theoreme de Siegel [24], ζK(1 − k) est un nombre rationnel si k est entier ⩾ 1; il est ≠ 0 si k est pair.…
On ℓ-adic representations and congruences for coefficients of modular forms (II)
The work I shall describe in these lectures has two themes, a classical one going back to Ramanujan [8] and a modern one initiated by Serre [9] and Deligne [3]. To describe the classical theme, let…
P-ADIC Properties of Modular Schemes and Modular Forms
This expose represents an attempt to understand some of the recent work of Atkin, Swinnerton-Dyer, and Serre on the congruence properties of the q-expansion coefficients of modular forms from the…
Analyse p-adique; secret Bourbaki Adaction
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By (1) above, f, and gi+Npm,p-,) differ multiplicatively in V by an element of 1+ nm+'V, so that f i -gi+xpm
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Les sch6mas de modules de courbes elliptiques Proc. of the 1972 Antwerp International Summer School on Modular Functions
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On Iadic representations and congruences for coefficients of modular forms
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    Pub. Math. I.H.E.S
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