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Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms

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Title: Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms
Description: Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods. By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.
Authors: Nicholas M. Katz
Resource Type: eBook.
Subjects: Convolutions (Mathematics), Mellin transform, Sequences (Mathematics)
Categories: MATHEMATICS / Number Theory, MATHEMATICS / Finite Mathematics, MATHEMATICS / Geometry / Algebraic, MATHEMATICS / Group Theory, MATHEMATICS / Probability & Statistics / General
Database: eBook Collection (EBSCOhost)
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 421488
RelevancyScore: 1044
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1044.26904296875
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  Data: Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms
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  Label: Description
  Group: Ab
  Data: Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods. By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.
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  Data: <searchLink fieldCode="DE" term="%22Convolutions+%28Mathematics%29%22">Convolutions (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mellin+transform%22">Mellin transform</searchLink><br /><searchLink fieldCode="DE" term="%22Sequences+%28Mathematics%29%22">Sequences (Mathematics)</searchLink>
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  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Number+Theory%22">MATHEMATICS / Number Theory</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Finite+Mathematics%22">MATHEMATICS / Finite Mathematics</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Geometry+%2F+Algebraic%22">MATHEMATICS / Geometry / Algebraic</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Group+Theory%22">MATHEMATICS / Group Theory</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Probability+%26+Statistics+%2F+General%22">MATHEMATICS / Probability & Statistics / General</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 515.723
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Convolutions (Mathematics)
        Type: general
      – SubjectFull: Mellin transform
        Type: general
      – SubjectFull: Sequences (Mathematics)
        Type: general
    Titles:
      – TitleFull: Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms
        Type: main
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          Name:
            NameFull: Nicholas M. Katz
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            NameFull: Nicholas M. Katz
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2012
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9780691153315
            – Type: isbn-print
              Value: 9780691153308
            – Type: isbn-electronic
              Value: 9781400842704
          Titles:
            – TitleFull: Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms
              Type: main
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