ClassNumberProblem.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

3 declarations, 2 contain sorry, 0 declared as axioms

Class number problem for real quadratic fields

Reference: Wikipedia

Imports (1)

FormalConjecturesUtil

Imported by 1 file

FormalConjectures/Subsets/FC100OpenSet1.lean

def ClassNumberProblem.IsClassNumberOne line 31 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Int
Proof uses: Exists, Irreducible, Polynomial, Rat, HSub.hSub, HPow.hPow, Nat, Polynomial.X, OfNat.ofNat, RingHom, Polynomial.C, Fact, Eq, NumberField.classNumber, AdjoinRoot
23 instances, coercions and auxiliary constants left out.
theorem ClassNumberProblem.class_number_problem There are infinitely many real quadratic fields ℚ(√d) with class number one, where d > 1 is a squarefree integer sorry line 41 source
Source documentation
There are infinitely many real quadratic fields ℚ(√d) with class number one, where d > 1 is a squarefree integer.

depends on sorry what this means
Statement uses: Set.Infinite, Int, Set.ofPred, And, Squarefree, GT.gt, OfNat.ofNat, ClassNumberProblem.IsClassNumberOne
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, Nat
7 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem class_number_problem :
    { d : ℤ | Squarefree d ∧ d > 1 ∧ IsClassNumberOne d }.Infinite := by
…
```
Mentions: ClassNumberProblem.IsClassNumberOne
theorem ClassNumberProblem.class_number_problem.variants.imaginary Documented declaration: imaginary sorry line 50 source
Source documentation
Stark–Heegner theorem : For any squarefree integer d < 0, the class number of the imaginary quadratic field Q(√d) is one if and only if d ∈ {-1, -2, -3, -7, -11, -19, -43, -67, -163}.

depends on sorry what this means
Statement uses: Eq, Set, Int, Set.ofPred, And, Squarefree, LT.lt, OfNat.ofNat, ClassNumberProblem.IsClassNumberOne, Insert.insert, Neg.neg, Singleton.singleton
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, Nat
13 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem class_number_problem.variants.imaginary :
    { d : ℤ | Squarefree d ∧ d < 0 ∧ IsClassNumberOne d } =
    {-1, -2, -3, -7, -11, -19, -43, -67, -163} := by
…
```
Mentions: ClassNumberProblem.IsClassNumberOne