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Primes of the Form $x^2 + Ny^2$: Fermat, Class Field Theory, and Complex Multiplication. Third Edition with Solutions (Chelsea Publications) - Tapa blanda
Sinopsis
This book studies when a prime $p$ can be written in the form $x^{2} + ny^{2}$. It begins at an elementary level with results of Fermat and Euler and then discusses the work of Lagrange, Legendre and Gauss on quadratic reciprocity and the genus theory of quadratic forms. After exploring cubic and biquadratic reciprocity, the pace quickens with the introduction of algebraic number fields and class field theory. This leads to the concept of ring class field and a complete but abstract solution of $p = x^{2} + ny^{2}$. To make things more concrete, the book introduces complex multiplication and modular functions to give a constructive solution. The book ends with a discussion of elliptic curves and Shimura reciprocity. Along the way the reader will encounter some compelling history and marvelous formulas, together with a complete solution of the class number one problem for imaginary quadratic fields.
The book is accessible to readers with modest backgrounds in number theory. In the third edition, the numerous exercises have been thoroughly checked and revised, and as a special feature, complete solutions are included. This makes the book especially attractive to readers who want to get an active knowledge of this wonderful part of mathematics.
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Acerca del autor
David A. Cox, Amherst College, MA.
"Sobre este título" puede pertenecer a otra edición de este libro.
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Primes of the Form $x^2 + ny^2$: Fermat, Class Field Theory, and Complex Multiplication. Third Edition with Solutions
Publicado por
American Mathematical Society, 2022
ISBN 10: 1470470284
ISBN 13: 9781470470289
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Condición: New. 2022. 3rd Edition. Paperback. . . . . . Nº de ref. del artículo: V9781470470289
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Primes of the Form $x^2 + ny^2$: Fermat, Class Field Theory, and Complex Multiplication. Third Edition with Solutions
Publicado por
American Mathematical Society, 2022
ISBN 10: 1470470284
ISBN 13: 9781470470289
Nuevo
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Librería: Kennys Bookstore, Olney, MD, Estados Unidos de America
Calificación del vendedor: 5 de 5 estrellas
Condición: New. 2022. 3rd Edition. Paperback. . . . . . Books ship from the US and Ireland. Nº de ref. del artículo: V9781470470289
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Primes of the Form $x^2 + Ny^2$
Publicado por
American Mathematical Society, US, 2022
ISBN 10: 1470470284
ISBN 13: 9781470470289
Nuevo
Paperback
Librería: Rarewaves.com UK, London, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
Paperback. Condición: New. 3rd. This book studies when a prime $p$ can be written in the form $x^{2} + ny^{2}$. It begins at an elementary level with results of Fermat and Euler and then discusses the work of Lagrange, Legendre and Gauss on quadratic reciprocity and the genus theory of quadratic forms. After exploring cubic and biquadratic reciprocity, the pace quickens with the introduction of algebraic number fields and class field theory. This leads to the concept of ring class field and a complete but abstract solution of $p = x^{2} + ny^{2}$. To make things more concrete, the book introduces complex multiplication and modular functions to give a constructive solution. The book ends with a discussion of elliptic curves and Shimura reciprocity. Along the way the reader will encounter some compelling history and marvelous formulas, together with a complete solution of the class number one problem for imaginary quadratic fields.The book is accessible to readers with modest backgrounds in number theory. In the third edition, the numerous exercises have been thoroughly checked and revised, and as a special feature, complete solutions are included. This makes the book especially attractive to readers who want to get an active knowledge of this wonderful part of mathematics. Nº de ref. del artículo: LU-9781470470289
Cantidad disponible: 3 disponibles
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Primes of the Form $x^2 + ny^2$ Fermat, Class Field Theory, and Complex Multiplication. Third Edition with Solutions
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Amer Mathematical Society, 2022
ISBN 10: 1470470284
ISBN 13: 9781470470289
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Paperback. Condición: Brand New. 3rd edition. 542 pages. 9.96x7.05x1.14 inches. In Stock. Nº de ref. del artículo: __1470470284
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Primes of the Form $x^2 + Ny^2$
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ISBN 10: 1470470284
ISBN 13: 9781470470289
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Primes of the Form $x^2 + ny^2$: Fermat, Class Field Theory, and Complex Multiplication. Third Edition with Solutions
Publicado por
American Mathematical Society, 2022
ISBN 10: 1470470284
ISBN 13: 9781470470289
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Primes in the Form X^2 + Ny^2 : Fermat, Class Field Theory, and Complex Multiplication, With Solutions
Publicado por
American Mathematical Society, 2022
ISBN 10: 1470470284
ISBN 13: 9781470470289
Nuevo
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Primes of the Form $x^2 + Ny^2$
Publicado por
American Mathematical Society, US, 2022
ISBN 10: 1470470284
ISBN 13: 9781470470289
Nuevo
Paperback
Librería: Rarewaves.com USA, London, LONDO, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
Paperback. Condición: New. 3rd. This book studies when a prime $p$ can be written in the form $x^{2} + ny^{2}$. It begins at an elementary level with results of Fermat and Euler and then discusses the work of Lagrange, Legendre and Gauss on quadratic reciprocity and the genus theory of quadratic forms. After exploring cubic and biquadratic reciprocity, the pace quickens with the introduction of algebraic number fields and class field theory. This leads to the concept of ring class field and a complete but abstract solution of $p = x^{2} + ny^{2}$. To make things more concrete, the book introduces complex multiplication and modular functions to give a constructive solution. The book ends with a discussion of elliptic curves and Shimura reciprocity. Along the way the reader will encounter some compelling history and marvelous formulas, together with a complete solution of the class number one problem for imaginary quadratic fields.The book is accessible to readers with modest backgrounds in number theory. In the third edition, the numerous exercises have been thoroughly checked and revised, and as a special feature, complete solutions are included. This makes the book especially attractive to readers who want to get an active knowledge of this wonderful part of mathematics. Nº de ref. del artículo: LU-9781470470289
Cantidad disponible: 3 disponibles
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Primes of the Form $x^2 + ny^2$ Fermat, Class Field Theory, and Complex Multiplication. Third Edition with Solutions
Publicado por
American Mathematical Society, 2022
ISBN 10: 1470470284
ISBN 13: 9781470470289
Nuevo
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Librería: moluna, Greven, Alemania
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Condición: New. Nº de ref. del artículo: 711092150
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Primes of the Form X^2 + Ny^2: Fermat, Class Field Theory, and Complex Multiplication, With Solutions (Ams Chelsea Publishing, 387)
Publicado por
American Mathematical Society, 2022
ISBN 10: 1470470284
ISBN 13: 9781470470289
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Condición: New. Nº de ref. del artículo: 401287570
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