arXiv subjects

Mirko Rösner

Publications and source records attributed to Mirko Rösner.

8 recordsLinked to original sources

arXiv2023

Global liftings between inner forms of GSp(4)

For reductive groups $G$ over a number field we discuss automorphic liftings from cuspidal irreducible automorphic representations $π$ of $G(\mathbb{A})$ to cuspidal irreducible automorphic representations on $H(\mathbb{A})$ for the quasi-split inner form $H$ of $G$. We show the existence of cohomological nontrivial weak global liftings in many cases. A priori these weak liftings do not give a description of the precise nature of the corresponding local liftings at the ramified places and in particular do not characterize the image of the lift. For inner forms of the group $H=\mathrm{GSp}(4)$ however we address these finer details. Especially, we prove the recent conjectures of Ibukiyama and Kitayama on paramodular newforms of squarefree level.

math.RT↗

arXiv2020

Spinor Euler factors for GSp(4) in the subregular case

For local non-archimedean fields $k$, Piatetski-Shapiro has defined local spinor $L$-factors for irreducible representations $Π$ of $\mathrm{GSp}(4,k)$ of dimension $>1$, attached to a choice of a Bessel model $Λ$. We classify regular poles that do not come from the asymptotic of the Bessel functions in the Bessel model. For anisotropic Bessel models there are no such subregular poles.

math.RT↗

arXiv2018

Exceptional poles of local spinor $L$-functions of $\mathrm{GSp}(4)$ with anisotropic Bessel models

For non-cuspidal irreducible admissible representations of $\mathrm{GSp}(4,k)$ over a local non-archimedean field $k$, we determine the exceptional poles of the spinor $L$-factor attached to anisotropic Bessel models by Piatetski-Shapiro.

math.RT↗

arXiv2018

Regular poles for spinor $L$-series attached to split Bessel models of $\mathrm{GSp}(4)$

For irreducible smooth representations $Π$ of $\mathrm{GSp}(4,k)$ over a non-archimedean local field $k$, Piatetskii-Shapiro and Soudry have constructed an $L$-factor depending on the choice of a Bessel model. It factorizes into a regular part and an exceptional part. We determine the regular part for the case of split Bessel models.

math.RT↗

arXiv2017

Multiplicity one for certain paramodular forms of genus two

We show that certain paramodular cuspidal automorphic irreducible representations of $\mathrm{GSp}(4,\mathbb{A}_\mathbb{Q})$, which are not CAP, are globally generic. This implies a multiplicity one theorem for paramodular cuspidal automorphic representations. Our proof relies on a reasonable hypothesis concerning the non-vanishing of central values of automorphic $L$-series.

math.RT↗

arXiv2016

Parahoric Restriction for GSp(4)

We determine the parahoric restriction of non-cuspidal irreducible smooth representations of GSp(4,F) for a local non-archimedean number field F.

math.RT↗

arXiv2016

Genericity under parahoric restriction

We study the preservation of genericity under parahoric restriction of depth zero representations.

math.RT↗

arXiv2014

Invariant Vectors for Weak Endoscopic and Saito-Kurokawa Lifts to GSp(4)

Let A be the adele ring over a totally real number field F. For cohomological cuspidal automorphic irreducible representations of GSp(4,A) coming from weak endoscopic or Saito-Kurokawa Lifts we determine the local invariant spaces under the first principal congruence subgroup at the non-archimedean places. For F=Q this gives rise to dimension formulas regarding certain subspaces of the inner cohomology of the genus two Shimura variety corresponding to the principal congruence subgroup level N=2. We prove the conjectures made by Bergström, Faber and van der Geer in a recent paper.

math.RT↗