20090102, 22:46  #1 
Aug 2004
Melbourne, Australia
2^{3}·19 Posts 
Birkhoff and Hall's theta function
Hi guys,
Long time no see. I've been busy doing a PhD (in combinatorial number theory), getting married and having a baby girl. (: So very little time to write. Anyway... Birkhoff and Hall's theta function is defined by for prime , and theta is multiplicative, that is if . (Sloane's A061350) I have shown that for prime , the largest such that dividing is . I suspect that this has already been found by someone else. So this is my "homework help." Does anyone know where I can find this? 
20090102, 22:59  #2  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,889 Posts 
Quote:
functions. You might also want to check Bruce Berndt's papers... Note: I am not very knowledgable about special functions.. 

20090105, 05:09  #3 
Aug 2004
Melbourne, Australia
2^{3}×19 Posts 
Thanks for that! I haven't found exactly what I was after but I think I'm getting a bit closer. I'm not 100% sure it has been published before, but I think there's a high chance (it's not a particularly surprising result).

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Requestion for fast chebyshev theta function  danaj  Computer Science & Computational Number Theory  9  20180331 14:59 
Trinity Hall Prime (from Numberphile)  TimSorbet  Lounge  3  20170908 06:18 
theta  davieddy  Math  2  20110802 09:50 
TPS Hall of Fame  Oddball  Twin Prime Search  3  20110630 19:06 
Connection between Li(x)Pi(x) and xtheta(x)  mart_r  Math  10  20110319 20:18 