Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593454 | Journal of Number Theory | 2016 | 12 Pages |
Abstract
In this paper, we introduce a Carlitz module analogue of the classical Euler totient function, and prove a function field analogue of Euler's theorem by using the Carlitz action and the Carlitz module analogue of the Euler totient function. We propose a function field analogue of Carmichael's totient function conjecture. In contrast to the classical case, we answer the function field analogue of Carmichael's conjecture in the negative. We also propose a function field analogue of Sierpiński's conjecture, and discuss some special cases of this analogue.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Nguyen Ngoc Dong Quan,