Book section
Ω in number theory
- Abstract:
- We present a new method for expressing Chaitin's random real, Ω, through Diophantine equations. Where Chaitin's method causes a particular quantity to express the bits of Ω by fluctuating between finite and infinite values, in our method this quantity is always finite and the bits of Ω are expressed in its fluctuations between odd and even values, allowing for some interesting developments. We then use exponential Diophantine equations to simplify this result and finally show how both methods can also be used to create polynomials which express the bits of Ω in the number of positive values they assume.
- Publication status:
- Published
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- Files:
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(Preview, Accepted manuscript, pdf, 139.5KB, Terms of use)
-
- Publisher copy:
- 10.1142/9789812770837_0010
- Publisher:
- World Scientific Publishing
- Pages:
- 161-173
- Series:
- Randomness and Complexity, From Leibniz to Chaitin
- Publication date:
- 2007-10-01
- DOI:
- ISBN:
- 9789812770820
- Language:
-
English
- Keywords:
- Pubs id:
-
1171660
- Local pid:
-
pubs:1171660
- Deposit date:
-
2021-05-05
Terms of use
- Copyright holder:
- World Scientific Publishing Co. Pte. Ltd.
- Copyright date:
- 2007
- Rights statement:
- Copyright © 2007 by World Scientific Publishing Co. Pte. Ltd.
- Notes:
- This is the accepted manuscript version of the chapter. The final version is available online from World Scientific Publishing at: https://doi.org/10.1142/9789812770837_0010
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