On trinomials over finite fields












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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.










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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


















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.










share|cite|improve this question











$endgroup$








  • 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
















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.










share|cite|improve this question











$endgroup$




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






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share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 19 at 20:53







Patrick Sole

















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
















  • 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












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