The Stark conjectures, introduced by Harold Stark beginning in 1971 and later expanded by John Tate, give conjectural information about the leading coefficient in the Taylor expansion of an Artin L-function attached to a Galois extension of algebraic number fields. They generalize the analytic class number formula, and in the abelian case with a simple zero, they predict the existence of Stark units generating abelian extensions of number fields.
Facts
StatementThe leading coefficient of an Artin L-function is the product of a regulator, the Stark regulator, with an algebraic number. 1 Proposed Year Progress Toward ResolutionProven only in special cases, such as when the character defining the L-function takes only rational values; the abelian conjectures remain unproven for most number fields. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Stark Conjectures (Wikipedia)
Sources
1. Stark Conjectures (Wikipedia)
Lead section
the leading coefficient of an Artin L-function is the product of a type of regulator, the Stark regulator, with an algebraic number.
Progress
Stark's principal conjecture has been proven in a few special cases, such as when the character defining the L-function takes on only rational values.
In Branch: Number Theory, Lead sentence
In number theory, the Stark conjectures, introduced by Stark (1971, 1975, 1976, 1980) and later expanded by Tate (1984), give conj
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