Related papers: On the Riemann Hypothesis

Theory of $n$-complements with applications is presented.

Through an equivalent condition on the Farey series set forth by Franel and Landau, we prove Riemann Hypothesis for the Riemann zeta-function and the Dirichlet L-function.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

Watson proved Kirkman's hypothesis (partially solved by Cayley). Using Lagrange Inversion, we drastically shorten Watson's computations and generalize his results at the same time.

Beginning from the resolution of Dirichlet L function, using the inner product formula of infinite-dimensional vectors in the complex space, the author proved the world's baffling problem--Generalized Riemann hypothesis.

In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.

We furnish an explicit bound for the prime number theorem in short intervals on the assumption of the Riemann hypothesis.

An technically interesting proof of a known theorem.

We provide an affirmative answer to a variant of the Busemann-Petty problem, proposed by V.~Milman: Let $K$ be a convex body in ${\mathbb R}^n$ and let $D$ be a compact subset of ${\mathbb R}^n$ such that, for some $1\ls k\ls n-1$,…

This work is dedicated to the promotion of the results Hadamard, Landau E., Walvis A., Estarmann T and Paul R. Chernoff for pseudo zeta functions. The properties of zeta functions are studied, these properties can lead to new regularities…

Approximation in measure is employed to solve an asymptotic Dirichlet problem on arbitrary open sets and to show that many functions, including the Riemann zeta-function, are universal in measure. Connections with the Riemann Hypothesis are…

The Riemann hypothesis is part of Hilbert's eighth problem in David Hilbert's list of 23 unsolved problems. it is also one of the Clay Mathematics Institute's Millennium Prize Problems. Some mathematicians consider it the most important…

In this paper, we consider the Dirichlet problem for a class of Hessian quotient equations on Riemannian manifolds. Under the assumption of an admissible subsolution, we solve the existence and the uniquness for the Dirichlet problem in a…

We present a replacement for traditional Riemann integrals in undergraduate calculus, which supplements naive precalculus and at the same time opens a way to more sophisticated theories such as Lebesgue integration.

We provide explicit bounds in the theory of the Riemann zeta-function at the line $\Re{s}=1$, assuming that the Riemann hypothesis holds until the height $T$. In particular, we improve some bounds, in finite regions, for the logarithmic…

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.

We have dealt with the Euler's alternating series of the Riemann zeta function to define a regularized ratio appeared in the functional equation even in the critical strip and showed some evidence to indicate the hypothesis. We briefly…

We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the…

Author of this article created for the first time the method for finding solutions of the Minkowski problem for closed surfaces in Riemannian space.

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.