On special Bessel periods and the Gross–Prasad conjecture for $$\mathrm {SO}(2n+1) \times \mathrm {SO}(2)$$

Furusawa, Masaaki; Morimoto, Kazuki

doi:10.1007/s00208-016-1440-z

Cited by 11 publications

(28 citation statements)

References 37 publications

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“…property without (Q) more generally for Hilbert-Siegel cusp forms. (4) Furusawa and Morimoto [12,13] have proved the hypothesis (Böch), provided κ > 2, ν is trivial and π is tempered. Since π is not a Saito-Kurokawa lift, Theorem 5 of [21] combined with [36] shows that π is tempered at least if κ > 2 and N is odd.…”

Section: Conjecture 11 the Characteristic Ideal Charmentioning

confidence: 89%

“…Thus C G 0 = 1 and B π 0 (ϕ 0 , φ0 ) = 2Λ(1, τ K/F ) in the notation of [25]. (3) Furusawa and Morimoto [12,13] have demonstrated Conjecture 9.1, provided that π is tempered, π v is square-integrable for every v ∈ Σ, Λ is the trivial character and the special Bessel period B 1 S is not zero on V . More generally, they proved the conjecture for such representations of SO(2n + 1) and the trivial character of SO (2).…”

mentioning

confidence: 99%

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Bessel periods and anticyclotomic $p$-adic spinor $L$-functions

Hsieh¹,

Yamana²

2018

Preprint

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Section: Conjecture 11 the Characteristic Ideal Charmentioning

confidence: 89%

mentioning

confidence: 99%

Bessel periods and anticyclotomic $p$-adic spinor $L$-functions

Hsieh¹,

Yamana²

2018

Preprint

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“…A sufficient nonvanishing result for the purpose of [23] follows from Waldspurger's treatment of half-integral weight modular forms [8,20]. Since the untwisted analogue in the case of genus 2 Siegel modular forms has now been established [1], there is hope to prove the following, stronger statement:…”

Section: A Conjecture In the Case Of Genusmentioning

confidence: 99%

Hyper-Algebras of Vector-Valued Modular Forms

Raum¹

2018

SIGMA

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We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of Q, acting on these hyper-algebras. These definitions bridge the classical and representation theoretic approach to Siegel modular forms. Combining both the product structure and the action of Hecke operators, we prove in the case of elliptic modular forms that all cusp forms of sufficiently large weight can be obtained from products involving only two fixed Eisenstein series. As a byproduct, we obtain inclusions of cuspidal automorphic representations into the tensor product of global principal series.

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“…[35,Section 7]), which is now known as "special Bessel models" (cf. [24], [8]). We verify that Sugano's local theory is applicable to the Fourier coefficients of the adelic cusp form for F f .…”

Section: Introductionmentioning

confidence: 99%

An explicit construction of non-tempered cusp forms on $$O(1,8n+1)$$

Narita

Pitale

2019

Ann. Math. Québec

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We explicitly construct cusp forms on the orthogonal group of signature (1, 8n + 1) for an arbitrary natural number n as liftings from Maass cusp forms of level one. In our previous works [28] and [21] the fundamental tool to show the automorphy of the lifting was the converse theorem by Maass. In this paper, we use the Fourier expansion of the theta lifts by Borcherds [4] instead.We also study cuspidal representations generated by such cusp forms and show that they are irreducible and that all of their non-archimedean local components are non-tempered while the archimedean component is tempered, if the Maass cusp forms are Hecke eigenforms. The standard L-functions of the cusp forms are proved to be products of symmetric square L-functions of the Hecke-eigen Maass cusp forms with shifted Riemann zeta functions.

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On special Bessel periods and the Gross–Prasad conjecture for $$\mathrm {SO}(2n+1) \times \mathrm {SO}(2)$$

Cited by 11 publications

References 37 publications

Bessel periods and anticyclotomic $p$-adic spinor $L$-functions

Bessel periods and anticyclotomic $p$-adic spinor $L$-functions

Hyper-Algebras of Vector-Valued Modular Forms

An explicit construction of non-tempered cusp forms on $$O(1,8n+1)$$

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