Diagonalization and Rationalization of algebraic Laurent series [article]

Boris Adamczewski, Jason P. Bell
2012 arXiv   pre-print
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
more » ... s on the number of variables, the degree of f and the height of f. This answers a question raised by Deligne.
arXiv:1205.4090v1 fatcat:smlmhbnkc5a73hcpwrvah5f7ha