Determinant formulas for zeta functions for real abelian function fields (Q764645)
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scientific article; zbMATH DE number 6014591
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Determinant formulas for zeta functions for real abelian function fields |
scientific article; zbMATH DE number 6014591 |
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Determinant formulas for zeta functions for real abelian function fields (English)
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13 March 2012
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There are many ``determinant formulas'' for class numbers of cyclotomic fields, the most famous perhaps being Maillet's determinant. \textit{M. Rosen} [Proc. Am. Math. Soc. 125, No. 5, 1299--1303 (1997; Zbl 0872.11045)] proved a similar formula for relative class numbers of cyclotomic function fields. In [Acta Arith. 138, No. 3, 259--268 (2009; Zbl 1228.11138)], the author explained these formulas by deriving a ``determinant formula'' for the zeta function of such fields in the special case of maximal real subfields of cyclotomic function fields. In this article, this result is generalized to arbitrary real subfields of cyclotomic function fields.
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cyclotomic function field
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Maillet determinant
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zeta function
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Carlitz module
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0.8943509459495544
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0.8625926971435547
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0.8370180726051331
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0.8291797041893005
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