Generating series of q-adic valuations are non-holonomic, non-algebraic over characteristic 0 fields, and take transcendental values at infinitely many rational and algebraic irrational points.
On the representation of C-recursive integer sequences by arithmetic terms
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We show that, if an integer sequence is given by a linear recurrence of constant rational coefficients, then it can be represented as the difference of two arithmetic terms with exponentiation, which do not contain any irrational constant. We apply our methods to various Lucas sequences including the classical Fibonacci sequence, to the sequence of solutions of the Pell equation and to some natural C-recursive sequences of degree 3.
citation-role summary
method 1
citation-polarity summary
fields
math.NT 1years
2024 1verdicts
CONDITIONAL 1roles
method 1polarities
use method 1representative citing papers
citing papers explorer
-
On non-holonomicity, transcendence and $p$-adic valuations
Generating series of q-adic valuations are non-holonomic, non-algebraic over characteristic 0 fields, and take transcendental values at infinitely many rational and algebraic irrational points.