Abstract
Following Iwasawa, we show how Stickelberger elements may be used to construct p-adic L-functions. The result yields a very useful representation of these functions in terms of a power series. As an application, we obtain information about the behavior of the p-part of the class number in a cyclo-tomic ℤ p -extension and prove that the Iwasawa α-invariant vanishes for abelian number fields. Also, we show how many of the formulas we obtain have analogues in the theory of function fields over finite fields.
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© 1982 Springer-Verlag New York Inc.
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Washington, L.C. (1982). Iwasawa’s Construction of p-adic L-functions. In: Introduction to Cyclotomic Fields. Graduate Texts in Mathematics, vol 83. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0133-2_7
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DOI: https://doi.org/10.1007/978-1-4684-0133-2_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0135-6
Online ISBN: 978-1-4684-0133-2
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