20090122, 00:06  #1 
Jan 2009
6_{16} Posts 
Chebyshev's Estimates
I've been working through Tenenbaum's book "Introduction to Analytic and Probabilistic Number Theory" and I'm stuck on the proof of an upper bound for .
For reference, it's Theorem 3 on page 11. The desired upper bound is Using the bound it's easy to show that for we have Tenenbaum then gives the bound So far, so good. At this point in the proof, Tenenbaum says "The stated result follows by choosing " and leaves the details to the reader. As much as I've looked at it, I still can't figure out how he arrives at the desired result. Any tips/suggestions? Thanks in advance. 
20090122, 12:48  #2  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}×937 Posts 
Quote:
This shouldn't be too bad. 

20090122, 17:21  #3 
Jan 2009
2×3 Posts 
Thanks for the suggestion, Dr. Silverman. When I made the substitution I wound up with a log(log(n)) term in the denominator that I'm not sure how to get rid of.
I tried estimating some more, but I still can't figure out where the factor of 8 in the term comes from. Thanks again, Dr. Silverman. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
The FibonacciChebyshev connection  Dr Sardonicus  Number Theory Discussion Group  6  20220115 12:13 
Requestion for fast chebyshev theta function  danaj  Computer Science & Computational Number Theory  9  20180331 14:59 
P1 B2 time estimates  henryzz  GMPECM  8  20091231 17:51 
GNFS estimates  10metreh  Factoring  48  20090408 01:54 
Msieve QS estimates  henryzz  Msieve  27  20090121 18:37 