Distribution of Smooth Numbers

flouran · 2009-12-24, 20:59

Is anyone aware of either Hildebrand's or Tenenbaum's work on the distribution of smooth numbers?

I have heard of their precise approximations for this distribution and thus was wondering if they were either in the form of papers and/or books? If the former, then please let me know of the title of the paper(s) (and if possible you can send me the electronic version of the paper(s) via email), and if the latter then please inform me of the title(s).

flouran · 2009-12-25, 03:18

To be more precise, what is the best lower-bound on $\Psi(x,y)$ ?

Anyone? It's awfully quite on this thread

retina · 2009-12-25, 03:24

Quote:

Originally Posted by flouran

Anyone? It's awfully quite on this thread

Considering the date I think you should give a little more time before declaring that everyone has abandoned you.

flouran · 2009-12-25, 03:25

Quote:

Originally Posted by retina

Considering the date I think you should give a little more time before declaring that everyone has abandoned you.

Any ideas then on the lower-bound?

retina · 2009-12-25, 03:32

Quote:

Originally Posted by flouran

Any ideas then on the lower-bound?

Is it 1? Or is it a trick question? For most mathematical problems I usually just use brute force, and if I haven't got the answer before reaching 10 I just give up. Perhaps this method will work for you also?

flouran · 2009-12-25, 03:33

Quote:

Originally Posted by retina

Is it 1? Or is it a trick question? For most mathematical problems I usually just use brute force, and if I haven't got the answer before reaching 10 I just give up. Perhaps this method will work for you also?

Not at all a trick question. Hopefully others will be able to contribute. If I find the answer myself, I shall post here.

Robert Holmes · 2009-12-25, 05:32

Not being an expert on the topic, this looks like a good place to start (if not just to harvest references):

"Smooth numbers: computational number theory and beyond"
http://www.math.leidenuniv.nl/~psh/ANTproc/09andrew.pdf

xilman · 2009-12-25, 08:50

Quote:

Originally Posted by retina

Considering the date I think you should give a little more time before declaring that everyone has abandoned you.

Why, what's happening?

I thought it was rather quiet, both on the forum and on the roads. No rush-hour traffic, even though most of the snow has now cleared from around here.

Very strange.

Paul

retina · 2009-12-25, 09:26

Quote:

Originally Posted by xilman

Why, what's happening?

I think it is flouran avoidance day. But don't tell him.

davieddy · 2009-12-25, 11:24

Quote:

Originally Posted by retina

I think it is flouran avoidance day. But don't tell him.

http://www.youtube.com/watch?v=TXdk4DOPgM8

davieddy · 2009-12-25, 13:28

Quote:

Originally Posted by retina

I think it is flouran avoidance day. But don't tell him.

I've just thought or a great title for my new book:

"How to win friends and influence people"

2009-12-24, 20:59	#1
flouran Dec 2008 7²·17 Posts	Distribution of Smooth Numbers Is anyone aware of either Hildebrand's or Tenenbaum's work on the distribution of smooth numbers? I have heard of their precise approximations for this distribution and thus was wondering if they were either in the form of papers and/or books? If the former, then please let me know of the title of the paper(s) (and if possible you can send me the electronic version of the paper(s) via email), and if the latter then please inform me of the title(s).

2009-12-25, 05:32	#7
Robert Holmes Oct 2007 1101010₂ Posts	Not being an expert on the topic, this looks like a good place to start (if not just to harvest references): "Smooth numbers: computational number theory and beyond" http://www.math.leidenuniv.nl/~psh/ANTproc/09andrew.pdf Last fiddled with by Robert Holmes on 2009-12-25 at 05:37

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2009-12-25, 03:18	#2
flouran Dec 2008 7²×17 Posts	To be more precise, what is the best lower-bound on $\Psi(x,y)$ ? Anyone? It's awfully quite on this thread