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algebra > abstract algebra > algebraic structure > field > Stark conjectures
number > number theory > algebraic number theory > Stark conjectures
... > mathematical analysis > calculus > series > Dirichlet series > Artin L-function > Stark conjectures
... > number > number theory > analytic number theory > L-function > Dirichlet series > Artin L-function > Stark conjectures
... > mathematical analysis > complex analysis > meromorphic function > L-function > Dirichlet series > Artin L-function > Stark conjectures

Preferred term

Stark conjectures  

Definition(s)

  • In number theory, the Stark conjectures, introduced by Stark (1971, 1975, 1976, 1980) and later expanded by Tate (1984), give conjectural information about the coefficient of the leading term in the Taylor expansion of an Artin L-function associated with a Galois extension K/k of algebraic number fields. The conjectures generalize the analytic class number formula expressing the leading coefficient of the Taylor series for the Dedekind zeta function of a number field as the product of a regulator related to S-units of the field and a rational number. When K/k is an abelian extension and the order of vanishing of the L-function at s = 0 is one, Stark gave a refinement of his conjecture, predicting the existence of certain S-units, called Stark units. Rubin (1996) and Cristian Dumitru Popescu gave extensions of this refined conjecture to higher orders of vanishing.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Stark_conjectures)

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