Related papers: On the Riemann Hypothesis and Hilbert's Tenth Prob…
A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral.
The Riemann hypothesis is identified with zeros of ${\cal N}=4$ supersymmetric gauge theory four-point amplitude. The zeros of the $\zeta(s)$ function are identified with th complex dimension of the spacetime, or the dimension of the…
It is developed the theory of the Dirichlet problem for harmonic functions. On this basis, for the nondegenerate Beltrami equations in the quasidisks and, in particular, in the smooth domains, it is proved the existence of regular solutions…
In this article, it is proved that the non-trivial zeros of the Riemann zeta function must lie on the critical line, known as the Riemann hypothesis.
The Riemann hypothesis, one of the most important open problems in pure mathematics, implies the most profound secret of prime numbers. One of the most interesting approaches to solve this hypothesis is to connect the problem with the…
We explore Hilbert space reformulations of Riemann Hypothesis developed by Nyman, Beurling, B\'{a}ez-Duarte, et. al. with a weighted Bergman space $\mathcal{H}=A_1^2(\mathbb{D})$, i.e., Riemann hypothesis holds if and only if the Hilbert…
In this paper, we used the principle of sieve function transformation to improve sieve method and the prime number theorem in the arithmetic sequence.For this, we proved General Riemann Hypothesis and Riemann Hypothesis to be true. further,…
An equivalent formulation of the Riemann hypothesis is given. The physical interpretation of the Riemann hypothesis equivalent formulation is given in the framework of quantum theory terminology. One more power series related to the Riemann…
For a ring R, Hilbert's Tenth Problem HTP(R) is the set of polynomial equations over R, in several variables, with solutions in R. We consider computability of this set for subrings R of the rationals. Applying Baire category theory to…
It is known that Hilbert's Tenth Problem over the Gaussian ring $\mathbb Z[i]=\{a+bi:\ a,b\in\mathbb Z\}$ is undecidable. In this paper we obtain the following further result: There is no algorithm to decide whether an arbitrarily given…
This survey presents some combinatorial problems with number-theoretic flavor. Our journey starts from a simple graph coloring question, but at some point gets close to a dangerous territory of the Riemann Hypothesis. We will mostly focus…
Finding hidden order within disorder is a common interest in material science, wave physics, and mathematics. The Riemann hypothesis, stating the locations of nontrivial zeros of the Riemann zeta function, tentatively characterizes…
In recent years, there has been some interest in applying ideas and methods taken from Physics in order to approach several challenging mathematical problems, particularly the Riemann Hypothesis. Most of these kind of contributions are…
The Riemann-Hilbert approach is extended to discuss the well-posedness of the nonlinear Schr\"odinger-Gerdjikov-Ivanon equation. The Lipschitz continuity of potential in $H^{2}(\mathbb{R})\cap H^{1,1}(\mathbb{R})$ to scattering data is…
In 1859, Riemann had announced the following conjecture : the nontrivial roots (zeros) $s=\alpha+i\beta$ of the zeta function, defined by: $$\zeta(s) =\displaystyle \sum_{n=1}^{+\infty}\frac{1}{n^s},\,\mbox{for}\quad \Re(s)>1$$ have real…
Hilbert's Irreducibility Theorem is a cornerstone that joins areas of analysis and number theory. Both the genesis and genius of its proof involved combining real analysis and combinatorics. We try to expose the motivations that led Hilbert…
Hypothesis of Riemann is rejected by definition, because {\zeta}(s), where s zeros of {\zeta}(s)=0, is not be equal by definition to the particular sum, which it assumes to be equal. R(s) = 1/2 holds only for the zeros of {\zeta}(s) = 0 and…
We introduce a Hamiltonian to address the Hilbert-P\'olya conjecture. The eigenfunctions of the introduced Hamiltonian, subject to the Dirichlet boundary conditions on the positive half-line, vanish at the origin by the nontrivial zeros of…
The transformations of the sum identities for generalized harmonic and oscillatory numbers, obtained earlier in our recent report [1], enable us to derive the new identities expressed in terms of the corresponding square roots of x. At…
We show that the $\theta=\infty$ conjecture implies the Riemann hypothesis.