Some Lacunary Power Series and Mahler's Um-numbers in p-adic Domain

Fatma Çalışkan
2022 Comptes Rendus de l'Academie Bulgare des Sciences / Proceedings of the Bulgarian Academy of Sciences  
In this paper, we consider some lacunar power series in Qp, where p is a prime number. We obtain some results about lacunary power series with rational coefficients for Um-number arguments in Qp. We determined whether the values of the considered lacunar power series belong to a certain field of algebraic numbers or to the set of transcendental numbers in Qp. Also, we find similar results for lacunary power series with p-adic algebraic coefficients.
doi:10.7546/crabs.2022.04.01 fatcat:xwjsgl5jtnfb7aox6ombb3rynq