Parahoric level p-adic L-functions for automorphic representations of GL_2n with Shalika models

2025/08/11 by Mladen Dimitrov, Dimitrov, Mladen, Andrei Jorza +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2508.08176

openalex publication_date 2025/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

We construct p-adic L-functions for regularly refined cuspidal automorphic representations of symplectic type on 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.

Citations

• On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces
• On p-adic L-functions for GL_2n in finite slope Shalika families
• A converse to a theorem of Gross, Zagier, and Kolyvagin
• On linear periods
• On p-adic L-functions for \rm GL(n)×\rm GL(n-1) over totally real fields
• Generic Transfer for General Spin Groups

Related

• On p-adic L-functions for GL_2n in finite slope Shalika families
• On the GL(2n) eigenvariety: branching laws, Shalika families and p-adic L-functions
• L-functions of GL(2n): p-adic properties and non-vanishing of twists
• P-adic L-functions for GL(3)
• Poles of p-adic Asai L-functions and distinguished representations