A note on transcendental analytic functions with rational coefficients mapping Q into itself

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F24%3A50021861" target="_blank" >RIV/62690094:18470/24:50021861 - isvavai.cz</a>

Result on the web

<a href="https://projecteuclid.org/journals/proceedings-of-the-japan-academy-series-a-mathematical-sciences/volume-100/issue-8/A-note-on-transcendental-analytic-functions-with-rational-coefficients-mapping/10.3792/pjaa.100.009.full" target="_blank" >https://projecteuclid.org/journals/proceedings-of-the-japan-academy-series-a-mathematical-sciences/volume-100/issue-8/A-note-on-transcendental-analytic-functions-with-rational-coefficients-mapping/10.3792/pjaa.100.009.full</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3792/pjaa.100.009" target="_blank" >10.3792/pjaa.100.009</a>

Result language

angličtina

Original language name

A note on transcendental analytic functions with rational coefficients mapping Q into itself

Original language description

In this note, the main focus is on a question about transcendental entire functions mapping Q into Q (which is related to a Mahler’s problem). In particular, we prove that, for any t &gt; 0, there is no a transcendental entire function f ∈ Q[[z]] such that f(Q) ⊆ Q and whose denominator of f(p/q) is O(qt), for all rational numbers p/q, with q sufficiently large.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Proceedings of the Japan Academy. Series A, Mathematical sciences

ISSN

0386-2194

e-ISSN

—

Volume of the periodical

100

Issue of the periodical within the volume

8

Country of publishing house

JP - JAPAN

Number of pages

3

Pages from-to

43-45

UT code for WoS article

001330419200001

EID of the result in the Scopus database

2-s2.0-85205798015