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Orders of a Quartic Field
 
Jin Nakagawa Joetsu University of Education
Orders of a Quartic Field
eBook ISBN:  978-1-4704-0168-9
Product Code:  MEMO/122/583.E
List Price: $42.00
MAA Member Price: $37.80
AMS Member Price: $25.20
Orders of a Quartic Field
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Orders of a Quartic Field
Jin Nakagawa Joetsu University of Education
eBook ISBN:  978-1-4704-0168-9
Product Code:  MEMO/122/583.E
List Price: $42.00
MAA Member Price: $37.80
AMS Member Price: $25.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1221996; 75 pp
    MSC: Primary 11

    In this book, the author studies the Dirichlet series whose coefficients are the number of orders of a quartic field with given indices. Nakagawa gives an explicit expression of the Dirichlet series. Using this expression, its analytic properties are deduced. He also presents an asymptotic formula for the number of orders in a quartic field with index less than a given positive number.

    Readership

    Graduate students and research mathematicians interested in number theory, specifically cubic and quartic extensions.

  • Table of Contents
     
     
    • Chapters
    • 0. Introduction
    • 1. Preliminaries
    • 2. Type 1111
    • 3. Types $112$ and $111^2$
    • 4. Types $22$, $21^2$ and $1^21^2$
    • 5. Types $13$ and $11^3$
    • 6. Types $4$ and $1^4$
    • 7. Type $2^2$
    • 8. Proof of Theorem 1
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1221996; 75 pp
MSC: Primary 11

In this book, the author studies the Dirichlet series whose coefficients are the number of orders of a quartic field with given indices. Nakagawa gives an explicit expression of the Dirichlet series. Using this expression, its analytic properties are deduced. He also presents an asymptotic formula for the number of orders in a quartic field with index less than a given positive number.

Readership

Graduate students and research mathematicians interested in number theory, specifically cubic and quartic extensions.

  • Chapters
  • 0. Introduction
  • 1. Preliminaries
  • 2. Type 1111
  • 3. Types $112$ and $111^2$
  • 4. Types $22$, $21^2$ and $1^21^2$
  • 5. Types $13$ and $11^3$
  • 6. Types $4$ and $1^4$
  • 7. Type $2^2$
  • 8. Proof of Theorem 1
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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