Quote:
Originally Posted by Dougy
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?

I expect that this might be found in Ramanujan's work on Theta
functions. You might also want to check Bruce Berndt's papers...
Note: I am not very knowledgable about special functions..