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The dilogarithm and the norm residue symbol. (English) Zbl 0493.12019

This paper contains a complete formula for the Hilbert Norm Residue Symbol, for cyclotomic extensions of q\(\mathbb Q_p\), which is of similar shape to Iwasawa’s incomplete formula [K. Iwasawa, J. Math. Soc. Japan 20, 151–165 (1968; Zbl 0256.12013)]. It is proven, essentially by verifying the Steinberg identity which in this context is a consequence of \(p\)-adic analytic properties of the dilogarithm series. The author is also able to deduce the non-degeneracy of the symbol directly from the formula.
Reviewer: Robert F. Coleman

MSC:

11S15 Ramification and extension theory
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)

Citations:

Zbl 0256.12013
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References:

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