20100706, 15:44  #1 
Aug 2006
3·1,987 Posts 
The constant in HardyLittlewood's Conjecture F
The HardyLittlewood Conjecture F includes calculation of the infinite product
where (I believe!) ranges over the primes and is the Jacobi symbol. Is there a good way to calculate this? Or, how can one calculate a reasonable number of decimal places of where ranges over the odd primes? (Recovering the original problem for any factorable a is easy.) 
20100706, 16:47  #2 
Aug 2006
3×1,987 Posts 
The problem can be solved if there are good ways to accelerate the calculation of sums over primes in congruence classes:
and for prime and integer m,n. Can this be done? Last fiddled with by CRGreathouse on 20100706 at 16:56 
20100706, 17:33  #3  
Apr 2010
94_{16} Posts 
Quote:


20100706, 17:34  #4 
Apr 2010
10010100_{2} Posts 

20100706, 17:47  #5 
Aug 2006
1011101001001_{2} Posts 
Thanks! I'll look it over.
(facepalm) Of course if I had a Mertens' Theoremlike estimate for and that would suffice. Last fiddled with by CRGreathouse on 20100706 at 17:59 
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