Related papers: The $\theta=\infty$ conjecture implies the Riemann…

Let $\Theta$ denote the supremum of the real parts of the zeros of the Riemann zeta function. We demonstrate that $\Theta=1$, which entails the existence of infinitely many Riemann zeros off the critical line (thus disproving the Riemann…

This analysis which uses new mathematical methods aims at proving the Riemann hypothesis and figuring out an approximate base for imaginary non-trivial zeros of zeta function at very large numbers, in order to determine the path that those…

We provide new sufficient conditions under which Ryser's conjecture holds.

We prove that the Riemann hypothesis is equivalent to the condition $\int_{2}^x\left(\pi(t)-\text{li}(t)\right)\mathrm{d}t<0$ for all $x>2$. Here, $\pi(t)$ is the prime-counting function and $\text{li}(t)$ is the logarithmic integral. This…

The Riemann Hypothesis is reformulated as statements about eigenvalues of some matrices entries of which are defined via Taylor coefficient of the zeta function. These eigenvalues demonstrate interesting visual patterns allowing one to…

We discuss the application of the determinantal method to the proof of the Riemann hypothesis. We start from the fact that, if a certain doubly infinite set of determinants are all positive, then the hypothesis is true. This approach…

Assuming the Riemann Hypothesis, we provide explicit upper bounds for moduli of $S(t)$, $S_1(t)$, and $\zeta\left(1/2+\mathrm{i}t\right)$ while comparing them with recently proven unconditional ones. As a corollary we obtain a conditional…

We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.

Using a result of recursive function theory and results of the complex analysis of Takeuti, which is based on a type theory and the work of Kreisel, and which gives a conservative extension of first order Peano arithmetic (PA), assuming all…

We prove that a certain conjecture holds true and the conjecture states a relationship between the zeta function of a finite category and the Euler characteristic of a finite category.

The GUE Hypothesis, which concerns the distribution of zeros of the Riemann zeta-function, is used to evaluate some integrals involving the logarithmic derivative of the zeta-function. Some connections are shown between the GUE Hypothesis…

In this paper, we prove a conjecture of Schnell in the surface case.

Identities involving Mobius function values (u(j),u(k)) are used to generate a Riemann Hypothesis equivalent.

In this short note, we give a proof of the Riemann hypothesis for Goss $v$-adic zeta function $\zeta_{v}(s)$, when $v$ is a prime of $\mathbb{F}_{q}[t]$ of degree one.

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

In this paper is stablished a characterization of the solutions of the equation: zeta(z) = 0. Then such a characterization is used to give a proof for Riemann is Conjecture.

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…

Assuming the Riemann Hypothesis it is proved that, for fixed $k>0$ and $H = T^\theta$ with fixed $0<\theta \le 1$, $$ \int_T^{T+H}|\zeta(1/2+it)|^{2k} dt \ll H(\log T)^{k^2(1+O(1/\log_3T))}, $$ where $\log_jT = \log(\log_{j-1}T)$. The proof…

We present a simple proof of the Riemann's Hypothesis (RH) where only undergraduate mathematics is needed.

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…