Related papers: On PNT equivalences for Beurling numbers
Correlations between spacelike separated measurements on entangled quantum systems are stronger than any classical correlations and are at the heart of numerous quantum technologies. In practice, however, spacelike separation is often not…
We present some new ideas on important problems related to primes. The topics of our discussion are: simple formulae for primes, twin primes, Sophie Germain primes, prime tuples less than or equal to a predefined number, and their…
The propositional logic is generalized on the real numbers field. the logical function with all properties of the classical probability function is obtained. The logical analog of the Bernoulli independent tests scheme is constructed. The…
We introduce p-equivalence by asymptotic probabilities, which is a weak almost-equivalence based on zero-one laws in finite model theory. In this paper, we consider the computational complexities of p-equivalence problems for regular…
This thesis determines some of the implications of non-universal and emergent universal statistics on arithmetic correlations and fluctuations of arithmetic functions, in particular correlations amongst prime numbers and the variance of the…
It is shown that the restrictions of what can be inferred from classically-recorded observational outcomes that are imposed by the no-cloning theorem, the Kochen-Specker theorem and Bell's theorem also follow from restrictions on inferences…
Prime number multiplet classifications and patterns are extended to negative integers. The extension from prime numbers to single prime powers is also studied. Prime number septets at equal distance are given. It is also shown that each…
We derived the sum identities for generalized harmonic and corresponding oscillatory numbers for which a sieve procedure can be applied. The obtained results enable us to understand better the properties of these numbers and their…
We present the formalization of Dirichlet's theorem on the infinitude of primes in arithmetic progressions, and Selberg's elementary proof of the prime number theorem, which asserts that the number $\pi(x)$ of primes less than $x$ is…
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a…
We introduce a concept of asymptotic principal values which enables us to handle rigorously singular integrals of higher-order poles encountered in the computation of various quantities based on correlation functions of a vacuum. Several…
Based on a generalization of Bohr's equivalence relation for general Dirichlet series, in this paper we study the sets of values taken by certain classes of equivalent almost periodic functions in their strips of almost periodicity. In…
Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are…
We show that polynomial time Turing equivalence and a large class of other equivalence relations from computational complexity theory are universal countable Borel equivalence relations. We then discuss ultrafilters on the invariant Borel…
A Borel equivalence relation on a Polish space is said to be countable if all of its equivalence classes are countable. Standard examples of countable Borel equivalence relations (on the space of subsets of the integers) that occur in…
By a suitable shifting-the-mean parametrization at the Dirichlet series level and Delange's Tauberian theorems, we show that the number of factors in random ordered factorizations of integers is asymptotically normally distributed.
A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral.
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…
Generalized Lelong numbers of plurisubharmonic functions with respect to plurisubharmonic weights (due to Demailly) are specified for weights with multicircled asymptotics. Explicit formulas for these values are obtained in terms of the…
The generalized Euler number E_{n|k} counts the number of permutations of {1,2,...,n} which have a descent in position m if and only if m is divisible by k. The classical Euler numbers are the special case when k=2. In this paper, we study…