High Quality Content by WIKIPEDIA articles! In number theory, the Stark conjectures, the first of which were introduced in a series of papers in the 1970s by American mathematician Harold Stark and later greatly expanded by John Tate, 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 give a vast generalization of 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. Extensions of this refined conjecture to higher orders of vanishing have been provided by Karl Rubin and Cristian Popescu.

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