<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We consider some lacunary power series with rational coefficients in 𝕈p. We show that under certain conditions these series take transcendental values at non-zero rational number arguments, and we determine the classes of these transcendental values with respect to Mahler’s classification of <italic>p</italic>-adic numbers.</p></abstract>

We consider some lacunary power series with rational coefficients in 𝕈p. We show that under certain conditions these series take transcendental values at non-zero rational number arguments, and we determine the classes of these transcendental values with respect to Mahler’s classification of p-adic numbers.

On Mahler’s <italic>p</italic>-adic <italic>S</italic>-, <italic>T</italic> -, and <italic>U</italic>-numbers

Faculty of Science, Department of Mathematics

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We consider some lacunary power series with rational coefficients in 𝕈p. We show that under certain conditions these series take transcendental values at...

On Mahler’s p-adic S-, T -, and U-numbers

Published Online: Apr 09, 2020

Page range: 81 - 94

Received: Mar 16, 2019

Accepted: Jul 15, 2019

DOI: https://doi.org/10.2478/auom-2020-0005

Keywords
Mahler’s classification of -adic numbers, -adic -number, -adic -number, -adic -number, transcendence measure

© 2020 Yann Bugeaud et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On Mahler’s p-adic S-, T -, and U-numbers

Published Online: Apr 09, 2020

Page range: 81 - 94

Received: Mar 16, 2019

Accepted: Jul 15, 2019

DOI: https://doi.org/10.2478/auom-2020-0005

KeywordsMahler’s classification of -adic numbers, -adic -number, -adic -number, -adic -number, transcendence measure

© 2020 Yann Bugeaud et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Mahler’s classification of -adic numbers, -adic -number, -adic -number, -adic -number, transcendence measure