-Yes Matt,i am not good at computers but i am pretty sure that there is an algorithm to calculate my integral numerically (tell me if i am wrong and this integral can not be calculated numerically) so we wouldn,t need to know the zeroes of Riemann function.
In fact can you calculate f(n) for...
-Mine is exact whereas the integral t/ln(t) is only an approximation,the Pi(x) is not easy to obtain i am giving an exact formula to calculate it.
-yes Matt but you have x(n)-x(n-1)=f(n) you don,t know how is the form of f(n) whereas the functions involved in my integral are known functions...
Sorry sometimes i make mistakes in writting, i meant that you could obtain the integral by using numerical methods,in fact the other approximation is made by integratin from 2 to x the function t/ln(t) wich can be only calculated numerically......i,m on the same case i think still the problem of...
But the integral can be calculated using the residue theorme or by numerical methods...so i don,t think it can be useful,it,s only an integral
By the way could you tell me where co7uld i find the finite -diference equation for prime number counting function..thanks.
here your are my last contribution to number theory, i tried to send it to several journals but i had no luck and i was rejected, i think journals only want famous people works and don,t want to give an oportunity to anybody.
the work is attached to this message in .doc format only use Mellin...
But making the change of variable c+iu the integral becomes simply a Fourier inverse transform (is a integral on the real plane of exp(iu)f(c+iu)exp(ct)) so if we can have a real integral and should be able to compute it numerically.
but what would happen if i try solving it numerically for example we should calculate the integral over all R of exp(ixt)f(c+ix)exp(ct) and this would be equal to our inverse Laplace transform, the problem is what c would i choose?..thanx.
let be e>0 but small so quantum gravity is renormalizable then what would be the calculation of mass and charge of it depending on e,now let,s take the limit e--->0 what would we have?...
Let,s suppose we want to get the inverse Laplace transform of a function f(s) numerically,we should calculate the integral from (c-i8,c+i8) of exp(st)f(s) my question is what c we should choose for calculating the integral?..wouldn,t depend the integral of the value of c..where could i find the...
let,s suppose we have to perform an integral into a infinite dimensional space,then we would use the Montecarlo,s Method as it is known to be independent of the dimension of the integral, but my problem is still the same..¿how do you define a point into a infinite dimensional space?...how would...
The question is interesting when related the generating function of MOebius function
Sum(n)mu(n)/n^(4-s)=R(4-s) where the sum is from 1 to infinite then according to our formula:
R(4-s)=M[w(x))/x^3] or M^-1[R(4-s)]=w(x)mu(x)/x^3 now integrating from k-1/2 to k+1/2 we have that...
let be the function given by f(x)=w(x)t^-3mu(x) where mu(x) is the Mobius function and w(x)=Sum(1<n<infinite)d(x-n) then my question is...does the Laplace transform of this function exist and is equal to
L[f(x)]=Sum(1<n<Infinite)mu(n)/n^3