Seminar
Parent Program: | |
---|---|
Location: | SLMath: Eisenbud Auditorium |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
We will show how to carry out a sieve of Erastosthenes up to $N$ in space $O(N^{1/3})$ and essentially linear time. This improves over the usual versions, which take space about $O(\sqrt{N})$ and essentially linear time. The algorithm -- which, like the one in (Galway, 2000), is ultimately related to diophantine approximation -- can also be used to factorize integers $n$, and thus to give the values of arithmetical functions such as the M\"obius function $\mu$ and the Liouville function $\lambda$ for all integers up to $N$.
No Notes/Supplements Uploaded No Video Files Uploaded