On the length of integers in telescopers for proper hypergeometric terms
Lily Yen, Capilano College
Abstract: We show that the number of digits in the integers of a creative telescoping relation of expected minimal order for a bivariate proper hypergeometric term has essentially cubic growth with the problem size. For telescopers of higher order but lower degree, we obtain a quintic bound. Experiments suggest that these bounds are tight. As applications of our results, we give an improved bound on the maximal possible integer root of the leading coefficient of a telescoper, and the first discussion of the bit complexity of creative telescoping. This is joint work with Manuel Kauers of RISC Linz, Austria.