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A canonical map between Hecke algebras

Andrea Mori, Lea Terracini (1999)

Bollettino dell'Unione Matematica Italiana

Sia D un corpo di quaternioni indefinito su Q di discriminante Δ e sia Γ il gruppo moltiplicativo degli elementi di norma 1 in un ordine di Eichler di D di livello primo con Δ . Consideriamo lo spazio S k Γ delle forme cuspidali di peso k rispetto a Γ e la corrispondente algebra di Hecke H D . Utilizzando una versione della corrispondenza di Jacquet-Langlands tra rappresentazioni automorfe di D × e di G L 2 , realizziamo H D come quoziente dell'algebra di Hecke classica di livello N Δ . Questo risultato permette di...

A generalization of level-raising congruences for algebraic modular forms

Claus Mazanti Sorensen (2006)

Annales de l’institut Fourier

In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field F . We do this for automorphic representations of an arbitrary reductive group G over F , which is compact at infinity. In the special case where G is an inner form of GSp ( 4 ) over , we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.

A p -adic measure attached to the zeta functions associated with two elliptic modular forms. II

Haruzo Hida (1988)

Annales de l'institut Fourier

Let f = n = 1 a ( n ) q n and g = n = 1 b ( n ) q n be holomorphic common eigenforms of all Hecke operators for the congruence subgroup Γ 0 ( N ) of S L 2 ( Z ) with “Nebentypus” character ψ and ξ and of weight k and , respectively. Define the Rankin product of f and g by 𝒟 N ( s , f , g ) = ( n = 1 ψ ξ ( n ) n k + - 2 s - 2 ) ( n = 1 a ( n ) b ( n ) n - s ) . Supposing f and g to be ordinary at a prime p 5 , we shall construct a p -adically analytic L -function of three variables which interpolate the values 𝒟 N ( + m , f , g ) π + 2 m + 1 < f , f > for integers m with 0 m < k - 1 , by regarding all the ingredients m , f and g as variables. Here f , f is the Petersson self-inner product of f .

An infinite ferm in the universal deformation space of Galois representations.

B. Mazur (1997)

Collectanea Mathematica

I hope this article will be helpful to people who might want a quick overview of how modular representations fit into the theory of deformations of Galois representations. There is also a more specific aim: to sketch a construction of a point-set topological'' configuration (the image of an infinite fern'') which emerges from consideration of modular representations in the universal deformation space of all Galois representations. This is a configuration hinted previously, but now, thanks to some...

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