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    Integral representation of Pi(x)/x^4

    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...
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    Quantum gravity in 4-e dimension

    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?...
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    Laplace inverse transform

    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...
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    Integral in an infinte dimensional space

    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? would...
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    Question on mu(x) function

    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
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    Is Special relativity quantizied?

    This is a special question, Sr quantizied?,in fact you will say yes but i don,t think so there are two reasons: a)Lorentz transforms say that a particle travelling at light speed has length 0,when in quantum string theory is asumed that exists a minimum quantity lp distance...
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    Some questions on GR

    a)Can we add extra terms with covariant derivative equal to 0 so the coupling constant in relativity is dimensionless?. b)for a metric gab that is time independent,can we define an "energy" term E so dE/dt is conserved?... c)from the Wheller-De Witt equation can we construct a linear...
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    Frame of reference

    given a frame of reference s In General Relativity in wich you meassure an interval of space dx, could we have another frame S`so the observer in that S`see that dx observed in S as a time interval dt?
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    Why plants are green?

    from a physical argument if plantes were black they would absorbe more energy from the sun then..why clorophile is green anbd why the plants are green?..
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    Is uncertaninty principle unbeatable?

    let suppose we have two observables A and B so its conmutator [A,B]=f(p,q) then let,s define a new observable C so [A,BC]=0 so we could measure A and BC with C a function of (q,p)the statement above is equivalent to (A,BC)=0 with () the Poisson Bracket then let,s put A=q and B=p then we must...
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    Dirac,s delta properties

    Dirac,s delta properties.... Let be d(x-a) the Delta function centered at x=a then could this function be approached by using a Fourier series on the interval (-pi,pi) with -Pi<a<Pi Anothe question.let be w(x)=sum(1<n<Infinite)d(x-n) then has the function z(x)=1/w(x) any sense and in teh...
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    Why Bohmian theory is bad?

    that,s the question..why bohmian mechanics is considered to be false and it is not accepted as a real interpretation of our quantum world?... If Bell,s inequality fails for Bohmian theory could somebody tell me why?..thanks. In fact i prefer Bohmian point of view rather than the ortodox...
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    Cauchy,s theorem in Real plane?

    i suppose all of us know the famous Cauchy,s formula Int(c)f(z)dz/(z-a)=(2pi)if(a) but could be applied the same to real plane,in fact let be the Integral over the closed path f(x,y)dxdy where f(x,y)=Gradient(g) then the integral in R^2 Int(C)f(x,y)dxdy/[x-a]=? where [x-a] means...
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    Problems with Riemann function

    let be the product R(s)R(s+a) with a a complex or real number..the i would like to know the limit Lim(s tends to e) being e a number so R(e)=0 ¿is there a number a so the limit is non-zero nor infinite?..thanks.
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    Dirichlet series inversion and prime number coutnign function

    Hello, i have developed a formula for inverting a dirichlet series ,and i apply to solve Phi(n),Mu(n) and d(n) arithmetical function,also i give a formula to obtain the Pi(n) function by means of a triple integral, the paper is in .doc format but if someone want to see it in .pdf can go to...
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    Questions in number theory

    let note f(x)=O(g(x)) this f(x)<MG(x) being M a constant then would it be true?.. If f(n)=o(n^u) then Sum(1<n<x)f(n)=O(n^u+1) adn Int(1,x)dnf(n)=O(n^u+1) Another question let be a(n)n^-s and b(n)n^-s two Dirichlet series so a(n)<b(n) for each n then if b(n)n^-s converges for a number...
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    Difficult integral

    I have problems calculating the integral (here 8 means infinite) Int(c-i8,c+i8)dsexp(sx)/sR(s) where R(sd) is Riemann,s function i make the change of variable s=c+iu so the new limits are Int(-8,8)iduexp(cx)exp(iu)/(c+iu)R(c+iu) now what numerical method could i use to calculate it?..thanks.
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    Dirichlet series inversion

    given the Dirichlet series Sum(0,infinite)a(n)n-^s=f(s) would be an analityc formula to invert the Dirichlet series to obtain a(n)?..i have searched it at google but found no results.
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    Green inverse problem in Differential equation

    Let be L(Y)=a0(x)D^2y+a1(x)Dy+a2(x) with the boundary conditions Y(a)=c and Y(b)=d then we could construct the Green function L(y)G(x,s)=d(x-s) then my question is if given the G(x,s) we could construct the L(y) operator considering is a second order differential equation.
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    Renormalize some theories

    why can we renormalize some theories but others not? fact what wo7uld happen if we apply renormalization group method,or Feynmann,s renormalization program to quatnum gravity (non renormalizable theories). I also found that they claim to have...
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    A string to dominate them all?

    According to lord of the rings..could be only a fundamental string that generates all the particles masses and all that?... where could i find an introduction to string theory?..thanks.
  22. E

    Generating function

    Let be a series Sum(0,infinite)anX^n=f(x) then could it be inverted to get the an? fact if we set x=1/Z the series becomes anZ^-n=Zeta transform of an so we could invert this (as seen in,could it be done to get the an?..thanks.
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    Moebius function

    I,am looking for several information about the moebius function.....specially its values for x equal to prime and if there is a relationship between this fucntion and the prime number coutnign function.
  24. E

    Integral equation of second kind and prime number counting function

    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...
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    Problem with a sum

    we know from basic number theory that Sum(1,x)1=[x] being [x] the integer part of x my problem is when we have the formula Sum(1,x)?=[Ax+b] being A and b arbitrary constant .. then ?=[ax+b]/[x] or not?..thanks.
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    A question

    A question .... Let suppose we have a function f(x) so Int(0.infinite)f(x)dx=N N finite number then my question is ..would be this f(x) a L^2(0,infinite) function so Int(0,infinite)[f(x)]^2dx is convergent?..thanks.
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    Methods for Non-renormalizable theories?

    I have some doubts when dealing with non-renormalizable theories in fact le,s suppose we have a theory that is non-renormalizable for n>4 or n=4 then we could do the trick of triying to renormalize it in 4-e dimension being e a small parameter e>0 and after that take the limit e=0 (dimensional...
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    Quantum mnechanics with lagrangians?

    usually quantum mechanics is made with hamiltonians but..could it be done with lagrangians in the sense that LF=gF where F is the wave function and g plays a role of an eigenvalue what would happen with dq/dtF? fact would it be equal to qEnF where En is the energy.. this can be...
  29. E

    Cuasi-exact Integral equation for Pi(x)/x 2

    Cuasi-exact Integral equation for Pi(x)/x**2 I thinks i have solved a cuasi exact integral equation for Pi(x)/x**2 expresing this function in terms of eigenfunctions of a symmetric kernel K(s,t)=nexp(-n**2(s-t)**2+s**2(t+s)/2**(5st)-1 form the usual integral equationfor Pi(x)...
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    More about Pi(x) and its derivatives

    studying the integral equation: log(R(s)/s=Int(0,infinite)Pi(x)/x(x**s-1) and derivating and itegrating i have got to set an integral equation for dPi(x)/dx but now i wuld like to know if dPi(x)/dx could be expanded into a series of eigenfunctions of the kernel so we could solve fact...