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.
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TheoremTwoValueBounds
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LeanPool.NairTenenbaum.Polynomials.PolynomialValueBounds
LeanPool.NairTenenbaum.Results.TheoremTwoStatement
Imported by
NairTenenbaum
.
exists_theoremTwo_value_cutoff
Fixed polynomial-value and prime-cutoff constants for Theorem 2
#
source
theorem
NairTenenbaum
.
exists_theoremTwo_value_cutoff
{
Q
:
Polynomial
ℤ
}
{
k
:
ℕ
}
(
hk
:
Q
.
natDegree
<
k
)
:
∃ (
A
:
ℝ
) (
C
:
ℝ
),
1
≤
A
∧
1
≤
C
∧
A
<
C
^
k
∧
(
2
≤
k
→
2
*
A
<
C
^
(
k
-
1
))
∧
∀ (
x
:
ℝ
),
1
≤
x
→
have
y
:=
x
^
(
↑
Q
.
natDegree
/
↑
k
);
∀
n
∈
shortInterval
x
y
,
↑
(
Polynomial.eval
(↑
n
)
Q
)
.
natAbs
≤
A
*
y
^
k