On the lifting of Hilbert cusp forms to Hilbert-Hermitian cusp forms

Yamana, Shunsuke

doi:10.1090/tran/8096

Cited by 2 publications

(1 citation statement)

References 29 publications

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“…The lifting constructions from smaller groups are typical ways to find examples of non-tempered cusp forms. For references in this direction we cite Oda [24], Rallis-Schiffmann [28], Ikeda [12,13], Ikeda-Yamana [14], Yamana [38,39] and Kim-Yamauchi [17] et al…”

Section: Introductionmentioning

confidence: 99%

An explicit lifting construction of CAP forms on O(1,5)

Narita¹,

Pitale²,

Wagh³

2022

Preprint

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We explicitly construct non-tempered cusp forms on the orthogonal group O(1,5) of signature (1+, 5−). Given a definite quaternion algebra B over Q, the orthogonal group is attached to the indefinite quadratic space of rank 6 with the anisotropic part defined by the reduced norm of B. Our construction can be viewed as a generalization of [22] to the case of any definite quaternion algebras, for which we note that [22] takes up the case where the discriminant of B is two. Unlike [22] the method of the construction is to consider the theta lifting from Maass cusp forms to O(1, 5), following the formulation by Borcherds. The cuspidal representations generated by our cusp forms are studied in detail. We determine all local components of the cuspidal representations and show that our cusp forms are CAP forms.

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Section: Introductionmentioning

confidence: 99%

An explicit lifting construction of CAP forms on O(1,5)

Narita¹,

Pitale²,

Wagh³

2022

Preprint

View full text Add to dashboard Cite

show abstract

An explicit lifting construction of CAP forms on O(1,5)

Narita

Pitale

Wagh

2023

Int. J. Number Theory

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In this paper, we explicitly construct nontempered cusp forms on the orthogonal group O(1,5) of signature [Formula: see text]. Given a definite quaternion algebra [Formula: see text] over [Formula: see text], the orthogonal group is attached to the indefinite quadratic space of rank 6 with the anisotropic part defined by the reduced norm of [Formula: see text]. Our construction can be viewed as a generalization of the previous work by the first two authors joint with Masanori Muto to the case of any definite quaternion algebras, for which we note that the work just mentioned takes up the case where the discriminant of [Formula: see text] is two. Unlike the previous work the method of the construction is to consider the theta lifting from Maass cusp forms to O(1,5), following the formulation by Borcherds. The cuspidal representations generated by our cusp forms are studied in detail. We determine all local components of the cuspidal representations and show that our cusp forms are CAP forms.

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On the lifting of Hilbert cusp forms to Hilbert-Hermitian cusp forms

Abstract: We construct a lifting that associates to a Hilbert cusp form a Hilbert-Hermitian cusp form. This is a generalization of the lifting of elliptic cusp forms constructed by Ikeda to arbitrary Hilbert cusp forms.

Cited by 2 publications

References 29 publications

An explicit lifting construction of CAP forms on O(1,5)

An explicit lifting construction of CAP forms on O(1,5)

An explicit lifting construction of CAP forms on O(1,5)

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