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Arithmetic of L-Functions

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Title: Arithmetic of L-Functions
Description: This volume brings together research and survey articles in algebraic number theory and arithmetic geometry. All of them share as a general theme the mysterious connections between special values of L-functions and algebraic invariants of Galois representations. These relationships are explored primarily through the lenses of Iwasawa theory and other Galois-equivariant points of view. The topics covered include the Galois module structure of ideal class groups, reciprocity laws in Iwasawa theory, Euler systems, p-adic L-functions, and étale cohomology – each of which has had a remarkable importance in the study of p-adic Galois representations over the last few decades. In addition, the final chapters of this volume serve as an introduction to the emerging subject of special L-values in positive characteristic. This is a new direction in the general area of global function field arithmetic that is concerned with the invariants of Galois representations valued in positive characteristic, as provided by Drinfeld modules or t-modules. Serving as the proceedings of an international conference held at ICMAT (Madrid) in May 2023, this volume is a useful resource for important techniques and approaches, as well as a source of concrete results and bibliographic references. It is of interest both to established researchers and to graduate students interested in algebraic number theory or in arithmetic geometry.
Authors: Dominik Bullach, Daniel Macías Castillo
Resource Type: eBook.
Categories: MATHEMATICS / Arithmetic, MATHEMATICS / Algebra / General, MATHEMATICS / Number Theory
Database: eBook Collection (EBSCOhost)
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  Data: Arithmetic of L-Functions
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  Data: This volume brings together research and survey articles in algebraic number theory and arithmetic geometry. All of them share as a general theme the mysterious connections between special values of L-functions and algebraic invariants of Galois representations. These relationships are explored primarily through the lenses of Iwasawa theory and other Galois-equivariant points of view. The topics covered include the Galois module structure of ideal class groups, reciprocity laws in Iwasawa theory, Euler systems, p-adic L-functions, and étale cohomology – each of which has had a remarkable importance in the study of p-adic Galois representations over the last few decades. In addition, the final chapters of this volume serve as an introduction to the emerging subject of special L-values in positive characteristic. This is a new direction in the general area of global function field arithmetic that is concerned with the invariants of Galois representations valued in positive characteristic, as provided by Drinfeld modules or t-modules. Serving as the proceedings of an international conference held at ICMAT (Madrid) in May 2023, this volume is a useful resource for important techniques and approaches, as well as a source of concrete results and bibliographic references. It is of interest both to established researchers and to graduate students interested in algebraic number theory or in arithmetic geometry.
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  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Arithmetic%22">MATHEMATICS / Arithmetic</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Algebra+%2F+General%22">MATHEMATICS / Algebra / General</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Number+Theory%22">MATHEMATICS / Number Theory</searchLink>
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    Languages:
      – Code: eng
        Text: English
    Titles:
      – TitleFull: Arithmetic of L-Functions
        Type: main
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          Name:
            NameFull: Dominik Bullach, Daniel Macías Castillo
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2025
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              Value: 9783985470846
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            – TitleFull: Arithmetic of L-Functions
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