The asymptotic distribution of Frobenius numbers

The Asymptotic Distribution of Frobenius Numbers

The Frobenius number F (a) of an integer vector a with positive coprime coefficients is defined as the largest number that does not have a representation as a positive integer linear combination of the coefficients of a. We show that if a is taken to be random in an expanding d-dimensional domain, then F (a) has a limit distribution, which is given by the probability distribution for the coveri...

Limiting Distribution of Frobenius Numbers for N = 3

A Heuristic Asymptotic Formula Concerning the Distribution of Prime Numbers

Suppose fx, h , ■ • ■ , fk are polynomials in one variable with all coefficients integral and leading coefficients positive, their degrees being h\ , h2, •• -, A* respectively. Suppose each of these polynomials is irreducible over the field of rational numbers and no two of them differ by a constant factor. Let Q(fx ,f2, • • • ,fk ; N) denote the number of positive integers n between 1 and N in...

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

Euler–frobenius Numbers and Rounding

We study the Euler–Frobenius numbers, a generalization of the Eulerian numbers, and the probability distribution obtained by normalizing them. This distribution can be obtained by rounding a sum of independent uniform random variables; this is more or less implicit in various results and we try to explain this and various connections to other areas of mathematics, such as spline theory. The mea...