On the Eisenstein series of Hilbert modular groups

Shimura, Goro

doi:10.1007/978-1-4612-2060-2_19

Cited by 4 publications

(4 citation statements)

References 13 publications

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“…These are due to Hecke when k ∈ Z. The proof for an arbitrary k ∈ 2 −1 Z, even in the Hilbert modular case, can be found in [20,Proposition A6.4] and [16].…”

Section: Additional Comments On Formula (21) and Some Remarksmentioning

confidence: 98%

Untitled

2006

Bull. Amer. Math. Soc.

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“…These are due to Hecke when k ∈ Z. The proof for an arbitrary k ∈ 2 −1 Z, even in the Hilbert modular case, can be found in [20,Proposition A6.4] and [16].…”

Section: Additional Comments On Formula (21) and Some Remarksmentioning

confidence: 98%

Untitled

2006

Bull. Amer. Math. Soc.

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“…Let E(0, K Γ ) be the subspace of E(0) consisting of K Γ -fixed Eisenstein series. By [19,Theorem 8.3], we have the isomorphism E(0, K Γ ) ∼ = E 1 (Γ) as a C-vector space by (2.2). We obtain the correspondence…”

Section: The Space Of Nearly Holomorphic Automorphic Formsmentioning

confidence: 99%

Nearly holomorphic automorphic forms on $\mathrm{SL}_2$

Horinaga¹

2019

Preprint

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We define the space of nearly holomorphic automorphic forms on a connected reductive group G over Q such that the homogeneous space G(R) 1 /K • ∞ is a Hermitian symmetric space. By Pitale, Saha and Schmidt's study, there are the classification of indecomposable (g, K∞)-modules which occur in the space of nearly holomorphic elliptic modular forms and Siegel modular forms of degree 2. This paper studies global representations of the adele group G(A Q ) which occur in the space of nearly holomorphic Hilbert modular forms. In the case of elliptic modular forms, the result of this paper is an adelization of Pitale, Saha and Schmidt's result.

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“…We shall restrict ourselves to the case m = 3, (p, q) = (2, 1) and to the Hilbert modular group Γ = Γ A = PSL(2, Ø) where Ø = Ø F is the ring of integers of a totally real field F of degree g ≥ 1 with class number 1. We repeatedly use facts about Eisenstein series from [16], [45], [46], [47], and [48]. The generalization to arbitrary class number and to arbitrary Γ A should be straightforward if somewhat technical, with some necessary material available in [54].…”

Section: Cuspidal Weyl Sums In the Hilbert Modular Casementioning

confidence: 99%

Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties

Cohen¹

2005

Duke Math. J.

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We generalize to Hilbert modular varieties of arbitrary dimension the work of W. Duke [14] on the equidistribution of Heegner points and of primitive positively oriented closed geodesics in the Poincaré upper half plane, subject to certain subconvexity results. We also prove vanishing results for limits of cuspidal Weyl sums associated with analogous problems for the Siegel upper half space of degree 2. In particular, these Weyl sums are associated with families of Humbert surfaces in Siegel 3-folds and of modular curves in these Humbert surfaces.Typeset November 6, 2018 [ 22:28 ] .

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On the Eisenstein series of Hilbert modular groups

Cited by 4 publications

References 13 publications

Untitled

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Nearly holomorphic automorphic forms on $\mathrm{SL}_2$

Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties

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