On the length of integers in telescopers for proper hypergeometric terms

Lily Yen, Capilano College

Tuesday November 5th, 2013, 2:30pm, K9509.


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.