Diagonalization and Rationalization of algebraic Laurent series
By Boris Adamczewski, Jason P. Bell. 2012
47 citations recorded by the source corpus.
We prove a quantitative version of a result of Furstenberg and Deligne stating that the the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime $p$ the reduction modulo $p$ of the diagonal of a multivariate algebraic power series $f$ with integer coefficients is an algebraic power series of degree at most $p^{A}$ and height at most $A^2p^{A+1}$, where $A$ is an effective constant that only depends on the number of variables, the degree of $f$ and the height of $f$. This answers a question raised by Deligne.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9897c6c8efe7c1ee2285bba259596fb0925d73ca
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In Algebra and Number Theory
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Citations in the corpus
- Analytic Combinatorics in Several Variables (2013, methodology): “More details can be found in Adamczewski and Bell (2012), which also gives a different, computationally effective, procedure for lifting. There are several older methods for computing asymptotics of D-finite generating functions, often used for computing diagonal asymptotics in the combinatorial lit”