Recent content by zetafunction

what are the differential equations associated to Riemann Hypothesis in this article ?? http://jp4.journaldephysique.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/jp4/abs/1998/06/jp4199808PR625/jp4199808PR625.html where could i find the article for free ? , have...

my question is if a Mac Donald function is really a Bessel function i mean J_{a}(ix)= CK_{a}(x) here 'C' is a complex number

if J_{u}(x) is a Bessel function.. do the following functions has special names ? a) J_{ia}(ib) here 'a' and 'b' are real numbers b) J_{ia}(x) the index is complex but 'x' is real c) J_{a}(ix) here 'x' is a real number but the argument of the Bessel function is complex.

um i forgot .. y(0)=0 assume there is an infinite potential barrier so the wave function must be 0 at the origin.

given the Schroedinger equation with an exponential potential -D^{2}y(x)+ae^{bx}y(x)-E_{n}y(x)= 0 with the boudnary conditons y(0)=0=y(\infty) is this solvable ?? what would be the energies and eigenfunction ? thanks.

can we simply truncate a Fourier series if it is divergent?? given a Fourier series of the form \sum_{n=0}^{\infty}\frac{cos(nx)}{\sqrt{n}} can i simply truncate this series up to some number finite N so i can get finite results ?? thanks.

let be N(x)= \sum_{n} H(x-E_{n}) the eingenvalue 'staircase' function and let be a system so V(x)=V(-x) and V^{-1}(x)=\sqrt \pi \frac{d^{1/2}}{dx^{1/2}} N(x) then would it be true that the two function \sum_{n}exp(-tE_{n})=Z(t)= \int_{0}^{\infty}dN(x)exp(-tx) and [tex]...

um.. if i use the fundamental theorem of the arithmetic to express m and n as a product of primes could i write or consider at least series over prime or prime powers ? i mean \sum_{m=-\infty}^{\infty}\sum_{p}f(p^{m}) in both case this sum is over prime and prime powers is this more or less...

it is possible to evaluate sums over the set of Rational so \sum_{q} f(q) with q= \frac{m}{n} and m and n are POSITIVE integers different from 0 ?? in any case for a suitable function is possible to evaluate \sum_{q} f(qx) with f(0)=0 ??

you can ALWAYS define the inverse of a function y=f(x) take the points (x,f(x)) and make a 'reflection' of these points alongside the line y=x you will get the NUMERICAL inverse of the function.

\xi (s) = \xi(1-s) with \frac{\xi(s)}{\xi(0)}= \frac{det(H+1/4-s(1-s))}{det(H+1/4)} with H= - \partial _{x}^{2}+ f(x) and f^{-1}(x)= \frac{2}{\sqrt \pi }\frac{d^{1/2}{dx^{1/2}}Arg (1/2+i \sqrt x ) http://vixra.org/abs/1111.0105

the Riemann Xi function(s) \xi(1/2+z) and \xi(1/2+iz) can be expressed as a functional determinant of a Hamiltonian operator, functional determinants may be evaluated by zeta regularization, using in both cases the Theta functions , semiclassical and spectral ones :)

have another question , if p \rightarrow infty , how can you prove that the infinite prime p= \infty is just the hole of the Real numbers ??

Riemann Hypothesis in the sense of Physics IS SOLVED http://vixra.org/pdf/1111.0105v2.pdf 1) operator -y''(x)+V(x)y(x)=E_{n}y(x) and y(x)=0=y(\infty) 2) V^{-1}(x)= 2 \sqrt \pi \frac{d^{1/2}N}{dx^{1/2}} 3) N(x) \pi = Arg\xi(1/2+i \sqrt x ) Bolte's semiclassical Law in physics

lostcauses10x .. i mean the imaginary part of the zeros ON THE CRITICAL STRIP 0<Re(s)<1