Towards a finite-slope universal Rankin-Selberg p-adic L-function

2025/12/01 by Gu, Haonan
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2512.01184

Abstract

This article studies the finite--slope analogue of Loeffler's conjectural framework for Rankin--Selberg p-adic L-functions in universal deformation families. Starting from residual representations ρ₁,ρ₂ of tame level~1 satisfying Hypothesis~3.1 of~\citeLoefflerUD, we consider the half--ordinary Panchishkin family (R,V,V⁺) of Example~3.17 of loc. cit., where the first factor varies in the ordinary Hida deformation and the second factor in the unrestricted universal deformation space.

Citations

• P-adic Rankin-Selberg L-functions in universal deformation families and functional equations
• On p-adic L-functions for GL_2n in finite slope Shalika families
• On extra-zeros of p-adic Rankin-Selberg L-functions
• Triple product p-adic L-functions associated to finite slope p-adic families of modular forms, with an appendix by Eric Urban
• Iwasawa theory of overconvergent modular forms, I: Critical p-adic L-functions
• Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality
• Cohomology of arithmetic families of (phi,Gamma)-modules
• Locally analytic distributions and p-adic representation theory, with applications to GL₂

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• On p-adic L-functions for \rm GL(n)×\rm GL(n-1) over totally real fields
• Rankin-Selberg Euler systems and p-adic interpolation