Related papers: On PNT equivalences for Beurling numbers
Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other…
Asymptotic expansions are given for large values of $n$ of the generalized Bernoulli polynomials $B_n^\mu(z)$ and Euler polynomials $E_n^\mu(z)$. In a previous paper L\'opez and Temme (1999) these polynomials have been considered for large…
We derive some important features of the standard quantum mechanics from a certain classical-like model -- prequantum classical statistical field theory, PCSFT. In this approach correspondence between classical and quantum quantities is…
We prove that neither a prime nor {an l-almost prime} number theorem hold in the class of regular Toeplitz subshifts. But, {when a quantitative strengthening of the regularity with respect to the periodic structure involving Euler's totient…
Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are…
Inspired by its fundamental importance in quantum mechanics, we define and study the notion of entanglement for abstract physical theories, investigating its profound connection with the concept of superposition. We adopt the formalism of…
We investigate the problem of the distribution of sums of functions of prime numbers located on an arithmetic progression. This problem is closely related to the problem of the distribution of prime numbers on an arithmetic progression.…
A celebrated analogy between prime factorizations of integers and cycle decompositions of permutations is explored here. Asymptotic formulas characterizing semismooth numbers (possessing at most several large factors) carry over to random…
A brief survey of some basic ideas of the so-called Idempotent Mathematics is presented; an "idempotent" version of the representation theory is discussed. The Idempotent Mathematics can be treated as a result of a dequantization of the…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
Exact summatory functions that count the number of prime $k$-tuples up to some cut-off integer are presented. Related summatory $k$-tuple analogs of the first and second Chebyshev functions are then defined. Using a gamma distribution…
We study the number of primes with a given primitive root and in an arithmetic progression under the assumption of a suitable form of the generalized Riemann Hypothesis. Previous work of Lenstra, Moree and Stevenhagen has given asymptotics…
We deduce the relative version of the equivalences relating the relative Local Global Principle and the Normality of the relative Elementary subgroups of the traditional classical groups, viz. general linear, symplectic and orthogonal…
Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in…
Let $\alpha$ and $\beta$ be two nonnegative integers such that $\beta < \alpha$. For an arbitrary sequence $\{a_n\}_{n\geqslant 1}$ of complex numbers, we consider the generalized Lambert series in order to investigate linear combinations…
We define a family {$\gamma(P)$} of generalized Euler constants indexed by finite sets of primes $P$ and study their distribution. These arise from partial sums of reciprocals of integers not divisible by any prime in $P$. An apparent…
Cloning, or approximate cloning, is one of basic operations in quantum information processing. In this paper, we deal with cloning of classical states, or probability distribution in asymptotic setting. We study the quality of the…
The propositional logic is generalized on the real numbers field. The logical analog of the Bernoulli independent tests scheme is constructed. The variant of the nonstandard analysis is adopted for the definition of the logical function,…
In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also…
If we assume the axiom of choice, then every two cardinal numbers are comparable. In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible…