On a generalization of the Maillet determinant. II (Q2759138)
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scientific article; zbMATH DE number 1680971
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a generalization of the Maillet determinant. II |
scientific article; zbMATH DE number 1680971 |
Statements
11 December 2001
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Maillet determinant
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Demyanenko matrix
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Chowla's problem
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Bernoulli polynomial
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polylogarithm
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Clausen function
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special values of the Dedekind zeta function
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On a generalization of the Maillet determinant. II (English)
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In part I [Number theory, Proc. intl. conf., Eger, Hungary, de Gryter, Berlin (1998; Zbl 0920.11071)] the authors introduced into the study of Maillet determinants a novel viewpoint, thinking of them as special values (or rather ``missing factors'' thereof) of the Dedekind zeta function of an imaginary subfield of \(\mathbb Q(\exp(2\pi i/m))\) at positive integral arguments. While in part I the main objective was to study Maillet determinants of Bernoulli type, in this part the authors make essential use of polylogarithms in order to consider Maillet determinants of Clausen type, as announced at the end of part I. Bernoulli type Maillet determinants alone do not suffice to express special values of the Dedekind zeta function, multiplication by Clausen type ones is needed, hence the name ``missing factor''.
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