An irrationality criterion for p-adic binomial series
by
Tapani Matala-aho
Matemaattisten tieteiden laitos/ Oulun yliopisto

Irrationality of certain values of the binomial series

Bq(z)= ∞ å k=0  æ è 1/q k ö ø zk,

in the p-adic fields will be investigated using Hensel's lemma and properties of the Diophantine equation x^q=1+z. It is interesting to note that Padé approximation method does not give irrationality results in all those cases, which can be handled by the method of this paper. But, when the both methods work we are able to get irrationality measures even for certain p-adic roots of unity. As an example we have the irrationality measure m₁₁(a)=3.636 for the fifht root of unity a ∈ Q₁₁ satisfying a ≡ 3 mod 11.

Date received: April 13, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacf-27.