- #1
eljose79
- 1,518
- 1
in this postcrpit i would like to say i have fund a second order integral equation (fredholm type) for the prime number counting function in particular for Pi(2^t)/2^2t function being Pi(t) the prime number counting function,teh equation is like this is we call Pi(2^t)/2^2t=g(t) then we have
g(s)+LnR(5s)/5s=Int(1,Infinite)K(s,t)g(t)dt for a certain symmetrical Kernel K(s,t) see the paper adjoint this Kernel is:
K(s,t)=nexp(-n^2(t-s)^2)+2^2(t+s)/2^5st-1
R(s) is Riemman,s Zeta function
with this calculating the prime number counting function is obvious,...just solve the integral equation by some approximate method to get Pi(2^2t)/2^2t
my results give an expresion for Pi(t) as
Pi(t)=Sum(n)a(n)fn(log2(t))
being fn(t) a set of orthonormal function...
yes,i treid to submit to journals but the snobbish referees (which only want famous names in the papers) did not give me a chance.
g(s)+LnR(5s)/5s=Int(1,Infinite)K(s,t)g(t)dt for a certain symmetrical Kernel K(s,t) see the paper adjoint this Kernel is:
K(s,t)=nexp(-n^2(t-s)^2)+2^2(t+s)/2^5st-1
R(s) is Riemman,s Zeta function
with this calculating the prime number counting function is obvious,...just solve the integral equation by some approximate method to get Pi(2^2t)/2^2t
my results give an expresion for Pi(t) as
Pi(t)=Sum(n)a(n)fn(log2(t))
being fn(t) a set of orthonormal function...
yes,i treid to submit to journals but the snobbish referees (which only want famous names in the papers) did not give me a chance.