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This paper presents some new statistical tests and new conjectures regarding the correspondence between the eigenvalues of random unitary matrices and the zeros of Riemann’s zeta function. Global fe...
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: For any real a>0 we determine the supremum of the real \sigma\ such that \zeta(\sigma+it) = a for some real t. For 0 < a < 1, a = 1, and a > 1 the results turn out to be quite different.} ...
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...
In this paper, we give a simple proof of the functional relation for the Lerch type Tornheim double zeta function. By using it, we obtain simple proofs of some explicit evaluation formulas for double ...
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.
For p prime, we give an explicit formula for Igusa’s local zeta function associated to a polynomial mapping f = (f1, . . . , ft) : Qn p ! Qt p,with f1, . . . , ft 2 Zp[x1, . . . , xn], and an integrat...
The transfer operator for $\Gamma_0(N)$ and trivial character $\chi_0$ possesses a finite group of symmetries generated by permutation matrices $P$ with $P^2=id$. Every such symmetry leads to a factor...
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...
We give two functional relations for the alternating analogues of Tornheim's double zeta function. Using the functional relations, we give new proofs of some evaluation formulas found by H. Tsumura fo...
We introduce a Bernoulli operator,let "B" denote the operator symbol,for n=0,1,2,3,... let ${B^n}: = {B_n}$ (where ${B_n}$ are Bernoulli numbers,${B_0} = 1,B{}_1 = 1/2,{B_2} = 1/6,{B_3} = 0$...).We o...
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...

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