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@article{764249,
author = {Greither, Cornelius and Kučera, Radan},
article_number = {1},
keywords = {Stark units; regulators; Gross conjecture on tori},
language = {eng},
issn = {0065-1036},
journal = {Acta Arithmetica},
title = {On a conjecture concerning minus parts in the style of Gross},
volume = {132},
year = {2008}
}
TY - JOUR
ID - 764249
AU - Greither, Cornelius - Kučera, Radan
PY - 2008
TI - On a conjecture concerning minus parts in the style of Gross
JF - Acta Arithmetica
VL - 132
IS - 1
SP - 1-48
EP - 1-48
SN - 00651036
KW - Stark units
KW - regulators
KW - Gross conjecture on tori
N2 - This paper is devoted to Gross's conjecture on tori over the base field Q. We call it the Minus Conjecture, since it involves a regulator built from units in the minus part. We recall and develop its relation to a conjecture of Burns, which is now known to hold generally in the absolutely abelian setting; however in many situations it is not clear at all how one should deduce the Minus Conjecture from it. We prove a somewhat weaker statement (order of vanishing) rather generally, and we give a proof of the Minus Conjecture for some specific classes of absolutely abelian extensions K/Q, for which K^+/Q is l-elementary and ramified in at most two primes. The field K is assumed to be of the form FK^+ where F is an arbitrary imaginary quadratic field. Our methods involve a good deal of explicit calculation; among other things, we use p-adic Gamma-functions and the Gross-Koblitz formula.
ER -
GREITHER, Cornelius and Radan KUČERA. On a conjecture concerning minus parts in the style of Gross. \textit{Acta Arithmetica}. 2008, vol.~132, No~1, p.~1-48. ISSN~0065-1036.
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