Symplectic periods of the continuous spectrum of \mathrm{GL}(2n)

Yamana, Shunsuke

doi:10.5802/aif.2890

Cited by 6 publications

(7 citation statements)

References 7 publications

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“…[Lan76,MW95]). In the case (G, H) = (GL 2n , Sp n ) this analysis (together with the results of [Yam14]) is propitiously sufficient for the precise description of L 2 H -dist (G(F )\G(A)). This is to a large extent due to the simple description of L 2 disc (G(F )\G(A)).…”

Section: Introductionmentioning

confidence: 85%

“…7.3. We will now use the results of Yamana [Yam14] (extending those of Jacquet-Rallis [JR92] and Offen [Off06a,Off06b]) on the symplectic periods of Eisenstein series to prove a strong form of the opposite inclusion of Proposition 7.1. For the next result, let P = M ⋉ U be a parabolic subgroup and π ∈ Π disc (A M \M(A)).…”

Section: The Distinguished Spectrummentioning

confidence: 99%

“…and almost all λ ∈ A. On the other hand, by [Yam14] [H] E(h, ϕ, λ) dh extends to a meromorphic function which is not identically zero for some ϕ ∈ AUT δ ′ (V(A)L\G(A)). We get a contradiction (e.g., using the Weierstrass preparation theorem).…”

Section: The Distinguished Spectrummentioning

confidence: 99%

“…disc,M H -dist (M(F )\M(A)) = ⊗L 2 disc,Sp n i -dist (GL 2n i (F )\ GL 2n i (A)) is described as above). The main input for this case is the results of Jacquet-Rallis, the second-named author and Yamana about symplectic periods of automorphic forms on GL 2n [JR92,Off06b,Off06a,Yam14]. In fact, we can formulate the same result for a variant of L 2 H -dist (G(F )\G(A)) where instead of pseudo Eisenstein series one uses a much bigger space (Corollary 7.7).…”

Section: Introductionmentioning

confidence: 98%

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On the distinguished spectrum of $Sp_{2n}$ with respect to $Sp_n\times Sp_n$

Lapid,

Offen

2015

Preprint

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Given a reductive group G and a reductive subgroup H, both defined over a number field F , we introduce the notion of the H-distinguished automorphic spectrum of G and analyze it for the pairs (GL 2n , Sp n ) and (Sp 2n , Sp n × Sp n ). In the first case we give a complete description using results of Jacquet-Rallis, Offen and Yamana. In the second case we give an upper bound, generalizing vanishing results of Ash-Ginzburg-Rallis and a lower bound, extending results of Ginzburg-Rallis-Soudry. Contents 1. Introduction 1 2. Notation and preliminaries 4 3. Double cosets 11 4. Intertwining Periods 28 5. H-periods of pseudo Eisenstein series 38 6. The distinguished spectrum 40 7. The case of (GL 2n , Sp n ) 45 8. The main result 51 References 60

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Section: Introductionmentioning

confidence: 85%

Section: The Distinguished Spectrummentioning

confidence: 99%

Section: The Distinguished Spectrummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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On the distinguished spectrum of $Sp_{2n}$ with respect to $Sp_n\times Sp_n$

Lapid,

Offen

2015

Preprint

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“…Relative truncation has also been employed to study the periods of the form Sp 2n ⊂ GL 2n in the work of Offen and Yamana [35,34,45]. Note that some regularization process is indispensable to study this case as periods of cusp forms vanish by the work of Jacquet and Rallis [22].…”

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confidence: 99%

Periods of automorphic forms over reductive subgroups

Zydor¹

2019

Preprint

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We present a regularization procedure of period integrals of automorphic forms on a group G over an arbitrary reductive subgroup G ′ ⊂ G. As a consequence we obtain an explicit G ′ (A)-invariant functional on the space of automorphic forms on G whose exponents avoid certain prescribed hyperplanes. We also provide a necessary and sufficient condition for convergence of period integrals of automorphic forms in terms of their exponents.

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Twisted symmetric square L-functions for $$\mathrm {GL}_n$$ GL n and invariant trilinear forms

Kaplan

Yamana

2016

Math. Z.

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Symplectic periods of the continuous spectrum of \mathrm{GL}(2n)

Cited by 6 publications

References 7 publications

On the distinguished spectrum of $Sp_{2n}$ with respect to $Sp_n\times Sp_n$

On the distinguished spectrum of $Sp_{2n}$ with respect to $Sp_n\times Sp_n$

Periods of automorphic forms over reductive subgroups

Twisted symmetric square L-functions for $$\mathrm {GL}_n$$ GL n and invariant trilinear forms

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