标题： 仿子群层次$p$-进制$L$-函数对于$\operatorname{GL}_{2n}$的自守表示的 Shalika 模型 显示英文标题

标题： Parahoric level $p$-adic $L$-functions for automorphic representations of $\operatorname{GL}_{2n}$ with Shalika models

摘要： 我们为对称型的正则细化的尖点自守表示在全实域上的$\operatorname{GL}_{2n}$构造了$p$-adic$L$-函数，这些表示在每个有限位置都是抛物球面的。 此外，我们证明了在这些点处抛物特征簇的平展性，并构造了族中的$p$-adic$L$-函数。 新颖的局部要素是改进的Ash--Ginzburg Shalika泛函的构造，以及将局部Zeta积分与超越球面层次的自守$L$-函数相关的Friedberg--Jacquet测试向量的产生。 我们的证明依赖于Shahidi的局部系数理论到Shalika模型的推广，为此我们建立了一个与外平方自守$L$-函数相关的通用分解公式。 显示英文摘要

摘要： We construct $p$-adic $L$-functions for regularly refined cuspidal automorphic representations of symplectic type on $\operatorname{GL}_{2n}$ over totally real fields, which are parahoric spherical at every finite place. Furthermore, we prove etaleness of the parabolic eigenvariety at such points and construct $p$-adic $L$-functions in families. The novel local ingredients are the construction of improved Ash--Ginzburg Shalika functionals and production of Friedberg--Jacquet test vectors relating local zeta integrals to automorphic $L$-functions beyond the spherical level. Our proofs rely on a generalization of Shahidi's theory of local coefficients to Shalika models, for which we establish a general factorization formula related to the exterior square automorphic $L$-function.