论文标题
未备份的$ {\ rm u} _ {2n+1} $和Rankin-Selberg Integrals的局部新形式
Local newforms for generic representations of unramified ${\rm U}_{2n+1}$ and Rankin-Selberg integrals
论文作者
论文摘要
最近，Atobe-oi-Yasuda建立了对非库赛局部本地领域的未受到的$ {\ rm u} _ {\ rm u} _ {\ rm u} _ {\ rm u} _ {\ rm u} _ {\ rm u} _ {\ rm u} $的新形式理论。在本文中，我们将其结果扩展到每个不可还原的通用表示形式，并计算OldForms空间的尺寸。我们还计算了在这些积分定义的$γ$ factor上的自然假设下附加到新形式和旧形式的Rankin-Selberg积分。
Recently Atobe-Oi-Yasuda established the newform theory for irreducible tempered generic representations of unramified ${\rm U}_{2n+1}$ over non-archimedean local fields. In this paper we extend their result to every irreducible generic representations and compute the dimensions of the spaces of oldforms. We also compute the Rankin-Selberg integrals attached to newforms and oldforms under a natural assumption on the $γ$-factors defined by these integrals.
