Related papers: Ordinality and Riemann Hypothesis I

The Schinzel Hypothesis is a conjecture about irreducible polynomials in one variable over the integers: under some standard condition, they should assume infinitely many prime values at integers. We consider a relative version: if the…

There have been a number of recent works on the theory of period polynomials and their zeros. In particular, zeros of period polynomials have been shown to satisfy a "Riemann Hypothesis" in both classical settings and for cohomological…

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 consider some applications of the theory of generalized Ore supplement conditions in the study of finite groups.

In this article we propose a revisitation of the well-known argument principle that may lead to the solution of the Riemann hypothesis. We are looking for collaborators.

Over any partially ordered abelian group whose positive cone is closed in an appropriate sense and has finitely many faces, modules that satisfy a weak finiteness condition admit finite primary decompositions. This conclusion rests on the…

We obtain necessary and sufficient conditions to characterize the boundedness of the composition of dyadic paraproduct operators.

We establish a sufficient condition for the ultimate positivity of P-recursive sequences of arbitrary order with a unique dominant root. By additionally verifying finitely many initial terms, the positivity can also be resolved. As an…

Assuming the Riemann hypothesis, we prove the latest explicit version of the prime number theorem for short intervals. Using this result, and assuming the generalised Riemann hypothesis for Dirichlet $L$-functions is true, we then establish…

In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…

Some new results concerning the equation $\sigma(N)=aM, \sigma(M)=bN$ are proved. As a corollary, there are only finitely many odd superperfect numbers with a fixed number of distinct prime factors.

In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the…

In the paper one proves a necessary condition for divisibility of integral elements by the powers of prime divisor of unramifed prime ideal and gives its application to a simple proof of Fermat's Last Theorem.

Four propositions are considered concerning the relationship between the zeros of two combinations of the Riemann zeta function and the function itself. The first is the Riemann hypothesis, while the second relates to the zeros of a…

We resolve Stillman's conjecture for families of polynomial rings that are graded by any semigroup under mild conditions. Conversely, we show that these conditions are necessary for the existence of a Stillman bound. This has applications…

We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide…

In this paper we provide a short proof of the Riemann Hypothesis for Drinfeld modules which uses only basic notions from the theory of global function fields and of Drinfeld modules.

"Goldbach's Conjecture" proven by analysis of how all combinations of the odd primes, summed in pairs, generates all of the even numbers.

We introduce the notion of corestricted free products of a family of profinite groups indexed over an arbitrary profinite space. Using arithmetic results of the second author, this enables us to prove an analogue of Riemann's existence…

We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.