Displaying similar documents to “Derivatives of L -functions at s = 0 (after Stark, Tate, Bienenfeld and Lichtenbaum)”

On the Jacobian criterion of formal smoothness.

Antonio G. Rodicio (1989)

Publicacions Matemàtiques

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We give a short proof of the Jacobian criterion of formal smoothness using the Lichtenbaum-Schlessinger cotangent complex.

A Stark conjecture “over 𝐙 ” for abelian L -functions with multiple zeros

Karl Rubin (1996)

Annales de l'institut Fourier

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Suppose K / k is an abelian extension of number fields. Stark’s conjecture predicts, under suitable hypotheses, the existence of a global unit ϵ of K such that the special values L ' ( χ , 0 ) for all characters χ of Gal / ( K / k ) can be expressed as simple linear combinations of the logarithms of the different absolute values of ϵ . In this paper we formulate an extension of this conjecture, to attempt to understand the values L ( r ) ( χ , 0 ) when the order of vanishing r may be greater than one. This conjecture...