Related papers: A simple proof of the generalized strong recurrenc…
The strong recurrence is equivalent to the Riemann hypothesis. On the other hand, the generalized strong recurrence holds for any irrational number. In this paper, we show the generalized strong recurrence for all non-zero rational numbers.…
In the present paper, we prove that self-approximation of $\log \zeta (s)$ with $d=0$ is equivalent to the Riemann Hypothesis. Next, we show self-approximation of $\log \zeta (s)$ with respect to all nonzero real numbers $d$. Moreover, we…
One of equivalents of the Riemann hypothesis is Li's criterion that all Li coefficients are positive. We study recurrence relations of Li coefficients in this note.
Recently, we have established the generalized Li's criterion equivalent to the Riemann hypothesis, viz. demonstrated that the sums over all non-trivial Riemann function zeroes k_n,a=Sum_rho(1-(1-((rho-a)/(rho+a-1))^n) for any real a not…
This short note presents a peculiar generalization of the Riemann hypothesis, as the action of the permutation group on the elements of continued fractions. The problem is difficult to attack through traditional analytic techniques, and…
A short proof of the equivalence of the recurrence of non-backtracking random walk and that of simple random walk on regular infinite graphs is given. It is then shown how this proof can be extended in certain cases where the graph in…
Recently, we have established the generalized Li's criterion equivalent to the Riemann hypothesis, viz. demonstrated that the sums over all non-trivial Riemann function zeroes k_n,b=Sum_rho(1-(1-((rho+b)/(rho-b-1))**n) for any real b not…
We prove a generalized version of the no-broadcasting theorem, applicable to essentially \emph{any} nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with ``super-quantum'' correlations.…
We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.
We prove a stronger version of Jarden's Theorem for recurrence of powers of recursive functions
We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic p L-series associated to function fields over a finite field. These analogs are based on the use of absolute…
We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations'…
We provide a strengthened version of the famous Jakobson's theorem. Consider an interval map $f$ satisfying a summability condition. For a generic one-parameter family $f_t$ of maps with $f_0=f$, we prove that $t=0$ is a Lebesgue density…
Fathi and Pageault have recently shown a connection between Auslander's generalized recurrent set $GR(f)$ and Easton's strong chain recurrent set. We study $GR(f)$ by examining that connection in more detail, as well as connections with…
In this paper, we give a short elementary proof of the well known Euler's recurrence formula for the Riemann zeta function at positive even integers and integral representations of the Riemann zeta function at positive integers and at…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.
A great number of articles widen a known scientific result $P(a)$ (such as: a theorem, an inequality, or a math/physics/chemical etc. proposition or formula) by a simple recurrence procedure and using, in the proof, the proposition $P(a)$…
Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to…
Using a structure theorem from [FG2010] we prove a version of multiple recurrence for sets of positive measure in a general stationary dynamical system.