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?
number-theory
asked Nov 15 at 4:04
sai
495
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up vote
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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?
number-theory
asked Nov 15 at 4:04
sai
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
add a comment |
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?
number-theory
asked Nov 15 at 4:04
sai
495
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
number-theory
asked Nov 15 at 4:04
sai
495
asked Nov 15 at 4:04
sai
495
asked Nov 15 at 4:04
sai
495
asked Nov 15 at 4:04
sai
495
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
add a comment |
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
add a comment |
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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