Exchanging the places p and infinity in the Leopoldt conjecture

2002/08/01 by Christopher Deninger, Deninger, Christopher
Mathematics · #11R18 #11R27 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11R18 #msc:11R27

paper · pdf · doi:10.48550/arxiv.math/0208008

arxiv created 2002/08/01 · openalex publication_date 2002/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Leopoldt conjecture is concerned with the image of the global units in the local units at the primes dividing p. In the definition of the global units the infinite place is distinguished. Exchanging p and infinity in the formulation one gets a new conjecture. It predicts that certain vectors should be linearly independent over the reals whose components are arguments of conjugates of Weil numbers. Using Baker's result on linear forms in logarithms we prove part of this new conjecture in certain abelian situations.

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