On the Iwasawa \(\lambda\)-invariants of imaginary quadratic fields (Q1302094)
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scientific article; zbMATH DE number 1335029
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Iwasawa \(\lambda\)-invariants of imaginary quadratic fields |
scientific article; zbMATH DE number 1335029 |
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On the Iwasawa \(\lambda\)-invariants of imaginary quadratic fields (English)
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12 June 2000
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Let \(p\) be an odd prime and \(k\) a complex quadratic number field, and let \(\lambda_p(k)\) denote Iwasawa's lambda-invariant of the cyclotomic \(\mathbb Z_p\)-extension of \(k\). Using an expression for the \(p\)-adic \(L\)-function due to \textit{W. Sinnott} [Invent. Math. 75, 273-282 (1984; Zbl 0531.12004)], the author reduces the computation of \(\lambda_p(k)\) to finding the first coefficient of the power series expansion of \(Q(T)\) not divisible by \(p\), where \(Q(T)\) is some explicitly given rational function of \(T\). Some worked examples are given.
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\(p\)-adic \(L\)-function
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Iwasawa invariant
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imaginary quadratic field
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