On the Gross-Stark Conjecture

2016/05/26 by Samit Dasgupta, Dasgupta, Samit, Mahesh Kakde +3
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Graph theory and applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1605.08169

openalex publication_date 2016/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1980, Gross conjectured a formula for the expected leading term at s=0 of the Deligne--Ribet p-adic L-function associated to a totally even character ψ of a totally real field F. The conjecture states that after scaling by L(ψω^-1, 0), this value is equal to a p-adic regulator of units in the abelian extension of F cut out by ψω^-1. In this paper, we prove Gross's conjecture.

Citations

• On ordinary ?-adic representations associated to modular forms

Related

• Comparing Two Formulas for the Gross-Stark Units
• On the rank one abelian Gross-Stark conjecture
• On a common refinement of Stark units and Gross-Stark units
• p-adic measures associated with zeta values and p-adic \log\n multiple gamma functions
• A p-adic Stark conjecture in the rank one setting