Exchanging the places p and infinity in the Leopoldt conjecture
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2002
 arXiv:
 arXiv:math/0208008
 Bibcode:
 2002math......8008D
 Keywords:

 Number Theory;
 11R18;
 11R27