Mixing
On trinomials over finite fields
1
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Is it true that the number of irreducible trinomials over F_q of degree at most n grows with n like n? See section 4 of
https://arxiv.org/pdf/1811.03789.pdf
for details, heuristic argument, and numerics.
polynomials finite-fields
asked Jan 19 at 20:27
Patrick SolePatrick Sole
1227
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add a comment |
1
$begingroup$
Is it true that the number of irreducible trinomials over F_q of degree at most n grows with n like n? See section 4 of
https://arxiv.org/pdf/1811.03789.pdf
for details, heuristic argument, and numerics.
polynomials finite-fields
asked Jan 19 at 20:27
Patrick SolePatrick Sole
1227
$endgroup$
1
$begingroup$
The number of all trinomials grows much faster.... You probably mean irreducible ones.
$endgroup$
– N. S.
Jan 19 at 20:29
$begingroup$
This sounds like a very difficult question. I agree with your heuristics. But the common results about the distribution of irreducibles (that I'm aware of) don't seem to bite at all at such a sparse family of polynomials. I'm sure the question has been studied. IIRC Lidl & Niederreiter say something about irreducible trinomials. People at MathOverflow may know more.
$endgroup$
– Jyrki Lahtonen
Jan 20 at 6:52
add a comment |
1
1
1
$begingroup$
Is it true that the number of irreducible trinomials over F_q of degree at most n grows with n like n? See section 4 of
https://arxiv.org/pdf/1811.03789.pdf
for details, heuristic argument, and numerics.
polynomials finite-fields
asked Jan 19 at 20:27
Patrick SolePatrick Sole
1227
$endgroup$
Is it true that the number of irreducible trinomials over F_q of degree at most n grows with n like n? See section 4 of
https://arxiv.org/pdf/1811.03789.pdf
for details, heuristic argument, and numerics.
polynomials finite-fields
polynomials finite-fields
asked Jan 19 at 20:27
Patrick SolePatrick Sole
1227
asked Jan 19 at 20:27
Patrick SolePatrick Sole
1227
edited Jan 19 at 20:53
Patrick Sole
asked Jan 19 at 20:27
Patrick SolePatrick Sole
1227
asked Jan 19 at 20:27
Patrick SolePatrick Sole
1227
asked Jan 19 at 20:27
Patrick SolePatrick Sole
1227
1227
1
$begingroup$
The number of all trinomials grows much faster.... You probably mean irreducible ones.
$endgroup$
– N. S.
Jan 19 at 20:29
$begingroup$
This sounds like a very difficult question. I agree with your heuristics. But the common results about the distribution of irreducibles (that I'm aware of) don't seem to bite at all at such a sparse family of polynomials. I'm sure the question has been studied. IIRC Lidl & Niederreiter say something about irreducible trinomials. People at MathOverflow may know more.
$endgroup$
– Jyrki Lahtonen
Jan 20 at 6:52
add a comment |
1
$begingroup$
The number of all trinomials grows much faster.... You probably mean irreducible ones.
$endgroup$
– N. S.
Jan 19 at 20:29
$begingroup$
This sounds like a very difficult question. I agree with your heuristics. But the common results about the distribution of irreducibles (that I'm aware of) don't seem to bite at all at such a sparse family of polynomials. I'm sure the question has been studied. IIRC Lidl & Niederreiter say something about irreducible trinomials. People at MathOverflow may know more.
$endgroup$
– Jyrki Lahtonen
Jan 20 at 6:52
1
1
$begingroup$
The number of all trinomials grows much faster.... You probably mean irreducible ones.
$endgroup$
– N. S.
Jan 19 at 20:29
$begingroup$
The number of all trinomials grows much faster.... You probably mean irreducible ones.
$endgroup$
– N. S.
Jan 19 at 20:29
$begingroup$
This sounds like a very difficult question. I agree with your heuristics. But the common results about the distribution of irreducibles (that I'm aware of) don't seem to bite at all at such a sparse family of polynomials. I'm sure the question has been studied. IIRC Lidl & Niederreiter say something about irreducible trinomials. People at MathOverflow may know more.
$endgroup$
– Jyrki Lahtonen
Jan 20 at 6:52
$begingroup$
This sounds like a very difficult question. I agree with your heuristics. But the common results about the distribution of irreducibles (that I'm aware of) don't seem to bite at all at such a sparse family of polynomials. I'm sure the question has been studied. IIRC Lidl & Niederreiter say something about irreducible trinomials. People at MathOverflow may know more.
$endgroup$
– Jyrki Lahtonen
Jan 20 at 6:52
add a comment |
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1
$begingroup$
The number of all trinomials grows much faster.... You probably mean irreducible ones.
$endgroup$
– N. S.
Jan 19 at 20:29
$begingroup$
This sounds like a very difficult question. I agree with your heuristics. But the common results about the distribution of irreducibles (that I'm aware of) don't seem to bite at all at such a sparse family of polynomials. I'm sure the question has been studied. IIRC Lidl & Niederreiter say something about irreducible trinomials. People at MathOverflow may know more.
$endgroup$
– Jyrki Lahtonen
Jan 20 at 6:52