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}·1,877 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).

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