On G-decimal Representation over Function Fields

DOI

10.2991/978-94-6463-463-1_10How to use a DOI?

Keywords

decimal representation; function field; combinatorics

Abstract

This paper discusses decimal representation over function field k_∞. Firstly, we provide definitions and establish existence of decimal representation over function fields. For function field k_∞, The work of L. Carlitz demonstrates that for the function field  k ∞ , { X α } X ∈ F q [ T ]  is uniformly distributed mod 1, where α ∈ k_∞ is an irrational element. This finding implies that arbitrary finite ordered set will occur infinitely often in the decimal representation of Xα. We present an upper bound of the “first” X, and our result is almost the best upper bound. The method we employ is purely combinatorial.

Copyright

© 2024 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Hong Ziwei
AU  - Zheng Zhiyong
PY  - 2024
DA  - 2024/08/02
TI  - On G-decimal Representation over Function Fields
BT  - Proceedings of the International Academic Summer Conference on Number Theory and Information Security (NTIS 2023)
PB  - Atlantis Press
SP  - 139
EP  - 147
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-463-1_10
DO  - 10.2991/978-94-6463-463-1_10
ID  - Ziwei2024
ER  -