5 papers
Asymptotics for partitions over the Fibonacci numbers and related sequences
Michael Coons, Simon Kristensen, Mathias L. Laursen
In this paper, harkening back to ideas of Hardy and Ramanujan, Mahler and de Bruijn, with the addition of more recent results on the Fibonacci Dirichlet series, we determine the as…
Transcendence criteria for infinite products of algebraic numbers
Mathias L. Laursen
Using an application of Schmidt's Subspace Theorem, this paper gives new transcendence criteria for rapidly converging infinite products of algebraic numbers. The paper also improv…
Algebraic independence of infinite series
Jaroslav Hancl, Mathias L. Laursen, Simon Kristensen
We give conditions on a finite set of series of rational numbers to ensure that they are algebraically independent. Specialising our results to polynomials of lower degree, we also…
Infinite products with algebraic numbers
Simon Kristensen, Mathias Løkkegaard Laursen
We obtain general criteria for giving a lower bound on the degree of numbers of the form or of the form $\prod_{m=1}^\infty \le…
Linear independence of continued fractions with algebraic terms
Jaroslav HanÄl, Mathias L. Laursen, Jitu Berhanu Leta
We give conditions on sequences of positive algebraic numbers , and number field to ensure that the numbers defined by the cont…