Journal article

The largest prime factor of $X^3+2$

Abstract:

The largest prime factor of $X^3+2$ has been investigated by Hooley, who gave a conditional proof that it is infinitely often at least as large as $X^{1+\delta}$, with a certain positive constant $\delta$. It is trivial to obtain such a result with $\delta=0$. One may think of Hooley's result as an approximation to the conjecture that $X^3+2$ is infinitely often prime. The condition required by Hooley, his R$^{*}$ conjecture, gives a non-trivial bound for short Ramanujan-Kloosterman sums. ...

Access Document

Files:
• (pdf, 284.0KB)

Authors

Publication date:
2001-01-01
UUID:
uuid:141ff1ff-9698-4f09-a74c-8cdeb78df8ce
Local pid:
oai:eprints.maths.ox.ac.uk:165
Deposit date:
2011-05-19