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L-values at Zero and the Galois Structure of Global Units

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Algebra

Part of the book series: Trends in Mathematics ((TM))

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Abstract

This article intends to present a comprehensive survey of the striking interplay between the Galois structure of the group of units in a number field and the values at zero of Artin L-functions. The algebraic ingredients come from integral representation theory, the ones from number theory include the Main Conjecture of Iwasawa theory. In fact, the discussion of recently defined invariants which go along with the unit group seems to propose possible generalizations of the Main Conjecture and fits very well into the framework of rather general conjectures regarding L-values by providing first affirmative answers. To begin with, we collect the principal ideas.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, D-86135, Augsburg, Germany

    Jürgen Ritter

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  1. Jürgen Ritter
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Editor information

Editors and Affiliations

  1. Centre for Advanced Study in Mathematics, Punjab University, Chandigarh, India

    I. B. S. Passi

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© 1999 Hindustan Book Agency (India) and Indian National Science Academy

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Ritter, J. (1999). L-values at Zero and the Galois Structure of Global Units. In: Passi, I.B.S. (eds) Algebra. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9996-3_10

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  • DOI: https://doi.org/10.1007/978-3-0348-9996-3_10

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9998-7

  • Online ISBN: 978-3-0348-9996-3

  • eBook Packages: Springer Book Archive

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