- #1
zetafunction
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- 0
can any Arithmetical function A(x)= \sum_{n\le x}a(n)
be regarded as the train of dirac delta functions (its derivative)
dA = \sum_{n=1}^{\infty}a(n)\delta (x-n)
from this definition could we regard the explicit formulae for chebyshev function
d\Psi(x) =1- \sum_{\rho}x^{\rho -1}- (x^{3}-x)^{-1}
and from this, using the definition of Mellin transform, we could obtain the sums over the Riemann zeros for lots of function f(x) provided its Mellin transform exists.
be regarded as the train of dirac delta functions (its derivative)
dA = \sum_{n=1}^{\infty}a(n)\delta (x-n)
from this definition could we regard the explicit formulae for chebyshev function
d\Psi(x) =1- \sum_{\rho}x^{\rho -1}- (x^{3}-x)^{-1}
and from this, using the definition of Mellin transform, we could obtain the sums over the Riemann zeros for lots of function f(x) provided its Mellin transform exists.