Related papers: On infinitely divisible distributions related to t…

In this paper, a positive answer to the Riemann hypothesis is given by using a new result that predict the exact location of zeros of the alternating zeta function on the critical strip.

Hardy's theorem for the Riemann zeta-function $\zeta(s)$ says that it admits infinitely many complex zeros on the line $\Re({s}) = \frac{1}{2}$. In this note, we give a simple proof of this statement which, to the best of our knowledge, is…

We give an interpretation of the Riemann hypothesis in terms of complex and topological dynamics. For example, the Riemann hypothesis is affirmative and all zeros of the Riemann zeta function are simple if and only if a certain meromorphic…

We investigate a dynamical basis for the Riemann hypothesis (RH) that the non-trivial zeros of the Riemann zeta function lie on the critical line x = 1/2. In the process we graphically explore, in as rich a way as possible, the diversity of…

The meromorphic function $W(s)$ introduced in the Riemann-Zeta function $\zeta(s) = W(s) \zeta(1-s)$ maps the line of $s = 1/2 + it$ onto the unit circle in $W$-space. $|W(s)| = 0$ gives the trivial zeroes of the Riemann-Zeta function…

Several arguments against the truth of the Riemann hypothesis are extensively discussed. These include the Lehmer phenomenon, the Davenport-Heilbronn zeta-function, large and mean values of $|\zeta(1/2+it)|$ on the critical line, and zeros…

This is a survey on weight enumerators, zeta functions and Riemann hypothesis for linear and algebraic-geometry codes.

We initiate the study of spectral zeta functions $\zeta_{X}$ for finite and infinite graphs $X$, instead of the Ihara zeta function, with a perspective towards zeta functions from number theory and connections to hypergeometric functions.…

We study the value-distribution of the Riemann zeta-function and related functions on and near the critical line. Amongst others, we focus on the following: The critical line is a natural boundary of the Voronin-type universality property…

We define a sequence of real functions which coincide with Li's coefficients at one and which allow us to extend Li's criterion for the Riemann Hypothesis to yield a necessary and sufficient condition for the existence of zero-free strips…

We present an unconditional proof that non-trivial zeros of the Riemann Zeta function must lie strictly on the critical line $\text{Re}(s) = 0.5$. By defining a recursive path of Taylor expansions originating from the domain of absolute…

Suppose that the Riemann hypothesis is false and $\rho_{*} = 1/2 + \eta_{*} + i \gamma_{*}$, $\eta_{*} > 0$, is a nontrivial zero of the Riemann $\zeta$-function off the critical line. Under the negation of the Riemann hypothesis for the…

We have given some arguments that a two-dimensional Lorentz-invariant Hamiltonian may be relevant to the Riemann hypothesis concerning zero points of the Riemann zeta function. Some eigenfunction of the Hamiltonian corresponding to…

The central idea of this article is to introduce and prove a special form of the zeta function as proof of Riemann's last theorem. The newly proposed zeta function contains two sub functions, namely $f_1(b,s)$ and $f_2(b,s)$. The unique…

We introduce a new Tauberian framework through the theory of "regular arithmetic functions". This allows us to establish a characterization of the Riemann hypothesis by linking the floor function to the distribution of nontrivial zeros of…

In this paper,we develop a novel representation of the zeta function expressed as the limiting difference between two structured double sums. This approach leads to a new and elegant identity involving maximum functions and additive terms,…

The paper describes a method for calculating values of Riemann's Zeta function within the critical strip 0< {\sigma} <1 and on its boundary. The approach is based on the "Alternating Zeta function" {\eta}(s). The actual Riemann Zeta…

This is a review of some of the interesting properties of the Riemann Zeta Function.

The Riemann Hypothesis is a conjecture that all non-trivial zeros of Riemann Zeta function are located on the critical line in the complex plane. Hundreds of propositions in function theory and analytic number theory rely on this…

We show that the Generalized Riemann Hypothesis for all Dirichlet L-functions is a consequence of certain conjectural properties of the zeros of the Riemann zeta function. Conversely, we prove that the zeros of $\zeta(s)$ satisfy those…