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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 a Radan KUČERA. On a conjecture concerning minus parts in the style of Gross. \textit{Acta Arithmetica}. 2008, roč.~132, č.~1, s.~1-48. ISSN~0065-1036.
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