About binary quadratic forms











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How many $operatorname{GL}_2(mathbb{Z})$-equivalence classes of integral binary quadratic forms of discriminant $-4$ are there? For example, the equivalence class of $x^2+y^2$ is one, what are the others?










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    That's it!${{}}$
    – Lord Shark the Unknown
    Nov 15 at 4:13










  • Why? Would you please explain.
    – sai
    Nov 15 at 5:10






  • 1




    @sal It follows from the reduction theory of binary quadratic forms. See Gauss's Disquisitiones Arithmeticae or any number of modern textbooks.
    – Lord Shark the Unknown
    Nov 15 at 7:27










  • So it is not an easy to prove result?
    – sai
    Nov 15 at 7:52










  • Start searching yourself! If you need a reference, here is a handout by Pete Clark.
    – Dietrich Burde
    Nov 15 at 9:22

















up vote
0
down vote

favorite












How many $operatorname{GL}_2(mathbb{Z})$-equivalence classes of integral binary quadratic forms of discriminant $-4$ are there? For example, the equivalence class of $x^2+y^2$ is one, what are the others?










share|cite|improve this question


















  • 1




    That's it!${{}}$
    – Lord Shark the Unknown
    Nov 15 at 4:13










  • Why? Would you please explain.
    – sai
    Nov 15 at 5:10






  • 1




    @sal It follows from the reduction theory of binary quadratic forms. See Gauss's Disquisitiones Arithmeticae or any number of modern textbooks.
    – Lord Shark the Unknown
    Nov 15 at 7:27










  • So it is not an easy to prove result?
    – sai
    Nov 15 at 7:52










  • Start searching yourself! If you need a reference, here is a handout by Pete Clark.
    – Dietrich Burde
    Nov 15 at 9:22















up vote
0
down vote

favorite









up vote
0
down vote

favorite











How many $operatorname{GL}_2(mathbb{Z})$-equivalence classes of integral binary quadratic forms of discriminant $-4$ are there? For example, the equivalence class of $x^2+y^2$ is one, what are the others?










share|cite|improve this question













How many $operatorname{GL}_2(mathbb{Z})$-equivalence classes of integral binary quadratic forms of discriminant $-4$ are there? For example, the equivalence class of $x^2+y^2$ is one, what are the others?







number-theory






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share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 15 at 4:04









sai

495




495








  • 1




    That's it!${{}}$
    – Lord Shark the Unknown
    Nov 15 at 4:13










  • Why? Would you please explain.
    – sai
    Nov 15 at 5:10






  • 1




    @sal It follows from the reduction theory of binary quadratic forms. See Gauss's Disquisitiones Arithmeticae or any number of modern textbooks.
    – Lord Shark the Unknown
    Nov 15 at 7:27










  • So it is not an easy to prove result?
    – sai
    Nov 15 at 7:52










  • Start searching yourself! If you need a reference, here is a handout by Pete Clark.
    – Dietrich Burde
    Nov 15 at 9:22
















  • 1




    That's it!${{}}$
    – Lord Shark the Unknown
    Nov 15 at 4:13










  • Why? Would you please explain.
    – sai
    Nov 15 at 5:10






  • 1




    @sal It follows from the reduction theory of binary quadratic forms. See Gauss's Disquisitiones Arithmeticae or any number of modern textbooks.
    – Lord Shark the Unknown
    Nov 15 at 7:27










  • So it is not an easy to prove result?
    – sai
    Nov 15 at 7:52










  • Start searching yourself! If you need a reference, here is a handout by Pete Clark.
    – Dietrich Burde
    Nov 15 at 9:22










1




1




That's it!${{}}$
– Lord Shark the Unknown
Nov 15 at 4:13




That's it!${{}}$
– Lord Shark the Unknown
Nov 15 at 4:13












Why? Would you please explain.
– sai
Nov 15 at 5:10




Why? Would you please explain.
– sai
Nov 15 at 5:10




1




1




@sal It follows from the reduction theory of binary quadratic forms. See Gauss's Disquisitiones Arithmeticae or any number of modern textbooks.
– Lord Shark the Unknown
Nov 15 at 7:27




@sal It follows from the reduction theory of binary quadratic forms. See Gauss's Disquisitiones Arithmeticae or any number of modern textbooks.
– Lord Shark the Unknown
Nov 15 at 7:27












So it is not an easy to prove result?
– sai
Nov 15 at 7:52




So it is not an easy to prove result?
– sai
Nov 15 at 7:52












Start searching yourself! If you need a reference, here is a handout by Pete Clark.
– Dietrich Burde
Nov 15 at 9:22






Start searching yourself! If you need a reference, here is a handout by Pete Clark.
– Dietrich Burde
Nov 15 at 9:22

















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