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On the Arakawa lifting Part I: Eichler commutation relations
Atsushi Murase, Hiro-aki Narita
We investigate the theta correspondence of cusp forms for the dual pair originally introduced by Tsuneo Arakawa in the non-adelic setting. We call this…
An explicit construction of non-tempered cusp forms on
Yingkun Li, Hiro-aki Narita, Ameya Pitale
We explicitly construct cusp forms on the orthogonal group of signature for an arbitrary natural number as liftings from Maass cusp forms of level one. In our previo…
Fourier expansion of Arakawa lifting II: Relation with central L-values
Atsushi Murase, Hiro-aki Narita
This is a continuation of our previous paper published in Israel J. Math 187 (2012), 317-369. The aim of the paper here is to study the Fourier coefficients of Arakawa lifts in rel…
Lifting to GL(2) over a quaternion division algebra and an explicit construction of CAP representations
Masanori Muto, Hiro-aki Narita, Ameya Pitale
The aim of this paper is to carry out an explicit construction of CAP representations of GL(2) over a division quaternion algebra with discriminant two. We first construct cusp for…