Square-free values of $n^2+1$

Details Square-free values of $n^2+1$ Square-free values of $n^2+1$

2010-10-29

arxiv.org/abs/1010.6217v1

Mathematics

Number Theory

Scientific paper

We show that there is a positive constant $c_0$ such that \[\sum_{n\le
x}\mu^2(n^2+1)c_0x+O_{\varepsilon}(x^{7/12+\varepsilon})\] for any fixed
$\varepsilon>0$. This improves a result of Estermann [3] from 1931, in which
the error term had an exponent $2/3$. The proof involves counting rational
points near an algebraic curve, which is done via the ``determinant method''.

Affiliated with

Also associated with

No associations

Rating

Square-free values of $n^2+1$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Square-free values of $n^2+1$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Square-free values of $n^2+1$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-615927