Timeline for Squareful values of polynomials
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 21, 2017 at 21:59 | comment | added | Dr. Pi | Hmm, I now think it is not as easy as I previously thought. I will return if I have more news. | |
| May 21, 2017 at 15:35 | comment | added | Daniel Loughran | That's nice, but the interesting case is when $\deg(f) > 2$; here one expects $f(n)$ to be squareful only finitely many times. | |
| May 21, 2017 at 13:10 | comment | added | Dr. Pi | I thought a bit more: One can try the square sieve approach for the set $\{bf(n):1\leq n \leq x, b^3|f(n), b\leq Y\}$. Then as long as $Y\leq x^{1-\epsilon}$ the square sieve works as in their book. This covers your question for the special case $\deg(f)=2$. | |
| May 21, 2017 at 7:50 | comment | added | Daniel Loughran | Sieving for squares is a much easier problem than sieving for squarefuls. All the sieves I have tried don't seem to work for squarefuls. If you are able to make your argument work I would be very interested, but you have somehow only dealt with the "easy" case when $b$ is small. | |
| May 21, 2017 at 0:46 | history | edited | Dr. Pi | CC BY-SA 3.0 |
added 698 characters in body
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| May 21, 2017 at 0:21 | history | answered | Dr. Pi | CC BY-SA 3.0 |