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- W165042595 abstract "The Dirichlet class number formula expresses the residue at s = 1 of the Dedekind zeta function ζ F(s) of an arbitrary algebraic number field F as the product of a simple factor (involving the class number of the field) with the determinant of a matrix whose entries are logarithms of units in the field. On the other hand, if F is a totally real number field of degree n, then a famous theorem by Klingen and Siegel says that the value ζ F (m) for every positive even integer in is a rational multiple of π mn In [52] and [53], a conjectural generalization of these two results was formulated according to which the special value ζ F (m) for arbitrary number fields F and positive integers m can be expressed in terms of special values of a transcendental function depending only on m, namely the m th classical polylogarithm function. These instances are expected to form part of a much more general picture in which a special value of an L-series of “motivic origin” is expressed in terms of some transcendental function. In this survey we collect some pieces fitting into and illustrating this picture." @default.
- W165042595 created "2016-06-24" @default.
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- W165042595 date "2000-01-01" @default.
- W165042595 modified "2023-09-23" @default.
- W165042595 title "Classical and Elliptic Polylogarithms and Special Values of L-Series" @default.
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- W165042595 doi "https://doi.org/10.1007/978-94-011-4098-0_21" @default.
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