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 ...
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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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Add this copy of Primes of the Form $x^2 + ny^2$: Fermat, Class Field to cart. $88.03, like new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2022 by American Mathematical Society.
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Fine. AMS Chelsea Publishing . Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Primes of the Form $x^2 + ny^2$: Fermat, Class Field to cart. $99.18, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2022 by American Mathematical Society.
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New. AMS Chelsea Publishing . Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Primes of the Form $x^2 + ny^2$: Fermat, Class Field to cart. $99.19, new condition, Sold by Booksplease rated 4.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2022 by American Mathematical Society.
Add this copy of Primes of the Form $x^2 + ny^2$: Fermat, Class Field to cart. $114.82, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by American Mathematical Society.
Add this copy of Primes of the Form $X^2 + Ny^2$: Fermat, Class Field to cart. $139.12, new condition, Sold by Kennys.ie rated 4.0 out of 5 stars, ships from Galway, IRELAND, published 2022 by American Mathematical Society.
