By Daniel Loebenberger,Michael Nüsken | published 2011-05-12 |
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We count ]B,C]-grained (ie. B-rough and C-smooth) integers. Our aim is to
exploit explicit versions of the prime number theorem as much as possible to
get good explicit bounds for the count of ]B,C]-grained integers. This analysis
was inspired by certain inner procedures in the general number field sieve. The
result should at least provide some insight in what happens there. We estimate
the given count in terms of some recursively defined functions. Since they are
still difficult to handle, only another approximation step reveals their
orders. Finally, we use the obtained bounds to visually show how good the
desired count can be approximated for the parameters of the general number
field sieve in the mentioned inspiring application.
... http://arxiv.org/abs/1003.2165
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