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By using new power inequalities we give an elementary proof of an important relation for the Riemann zeta-function |\zeta(1-s)| <= |\zeta(s)| in the strip 0< Re s<1/2,\ |\Im s| >= 12. Moreover, we est...
Abstract: It is proved that some set of the values of $|\zeta(\sigma_0+i\vp_1(t))|^2$ on every fixed line $\sigma=\sigma_0>1$ generates a corresponding set of the values of $|\zeta(\frac 12+it)|^2$ on...
Abstract: New recursion relations for the Riemann zeta function are introduced. Their derivation started from the standard functional equation. The new functional equations have both real and imaginar...
We study the distribution of graded degrees of freedom in classically stable oriented closed string vacua and use the Rankin-Selberg transform to link it to the nite one-loop vacuum energy.
Renormdynamic equations of motion and their solutions are given. New equation for NBD distribution and Riemann zeta function invented. Explicit forms of the z-Scaling functions are constructed.
Some statements concerning the distribution of imaginary parts of zeros of the Riemann zeta\,-function are established. These assertions are connected with so\,-called `Gram's law' or `Gram's rule'. I...
The Riemann Zeta function ζ(s) can be expressed in terms of the entire function ξ(s)which has an integral representation characteristic of a general class of entire functions symmetric around s = &fr...
We derive an expansion for the Riemann zeta function ζ(s) involving incomplete gamma functions with their second argument proportional to n2p, where n is the summation index and p is a positive intege...
We show that the function f(z) : = \frac{z}{1-z} z (\frac{1}{1-z}), |z| < 1, belongs to the Hardy class Hp if and only if 0 < p < 1.

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