2020/07/20 by Santiago Molina Blanco, Blanco, Santiago Molina
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.2007.09984
openalex publication_date 2020/07/20 · arxiv created 2020/10/28 · arxiv updated 2020/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we propose a new construction of cyclotomic p-adic L-functions attached to classical modular cuspidal eigenforms. This allows us to cover most known cases to date and provides a method which is amenable to generalizations to automorphic forms on arbitrary groups. In the classical setting of GL2 over Q this allows us to construct the p-adic L-function in the so far uncovered extremal case which arises under the unlikely hypothesis that p-th Hecke polynomial has a double root. Although Tate's conjecture implies that this case should never take place for GL2/Q, the obvious generalization does exist in nature for Hilbert cusp forms over totally real number fields of even degree and this article proposes a method which should adapt to this setting. We further study the admissibility and the interpolation properties of these extremal p-adic L-functions, and relate them to the two-variable p-adic L-function interpolating cyclotomic p-adic L-functions along a Coleman family.