4 papers
Power Partitions and Hayman Functions
José L. Fernández, Víctor J. Maciá
We prove, within the probabilistic framework of Khinchin families, that the generating function of partitions into -th powers is strongly Gaussian in the sense of Báez-Dua…
Counting coprime pairs in random squares
José L. Fernández, Pablo Fernández
Extending the classical Dirichlet's density theorem on coprime pairs, in this paper we describe completely the probability distribution of the number of coprime pairs in random squ…
Growth of power series with nonnegative coefficients, and moments of power series distributions
Alicia Cantón, José L. Fernández, Pablo Fernández +1
Any power series with nonnegative coefficients has an associated family of probability distributions supported on the nonnegative integers. There is a close connection between the…
Large Powers asymptotics, Khinchin families and Lagrangian distributions
José L. Fernández, Víctor J. Maciá
This paper delves on the versatility of the theory of Khinchin families for asymptotic estimation. We show that in combination with Local Central Limit theorems for lattice variabl…