Journal article
Iteration of quadratic polynomials over finite fields
- Abstract:
- For a finite field of odd cardinality $q$, we show that the sequence of iterates of $aX2+c,$ starting at $0$, always recurs after $O(q/loglogq)$ steps. For $X2+1$ the same is true for any starting value. We suggest that the traditional "Birthday Paradox" model is inappropriate for iterates of $X3+c,$ when $q$ is 2 mod 3.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Accepted manuscript, pdf, 232.8KB)
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- Publisher copy:
- 10.1112/S0025579317000328
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Authors
Bibliographic Details
- Publisher:
- Cambridge University Press Publisher's website
- Journal:
- Mathematika Journal website
- Volume:
- 63
- Issue:
- 3
- Pages:
- 1041-1059
- Publication date:
- 2017-11-29
- Acceptance date:
- 2017-03-29
- DOI:
- EISSN:
-
2041-7942
- ISSN:
-
0025-5793
- Source identifiers:
-
687410
Item Description
- Pubs id:
-
pubs:687410
- UUID:
-
uuid:4019b5ed-b4e7-46f0-aa75-51fc391f5f69
- Local pid:
- pubs:687410
- Deposit date:
- 2017-03-29
Terms of use
- Copyright holder:
- University College London
- Copyright date:
- 2017
- Notes:
- Copyright © 2017 University College London. This is the accepted manuscript version of the article. The final version is available online from Cambridge University Press at: https://doi.org/10.1112/S0025579317000328
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