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cloud.google.com·8h ago
AI Research
arXiv CS.AI·25d ago·5 min read
Constrained PSLQ Search for Machin-like Identities Achieving Record-Low Lehmer Measures
TL;DR
A new framework combines the PSLQ integer-relation algorithm with number-theoretic filters to discover Machin-like arctangent relations for computing π, achieving record-low Lehmer measures of 1.4572 and 1.3291. This method enables the generation of longer mathematical identities efficiently.
✦ Why It Matters
Explore this new framework to enhance your own mathematical identity searches and computations.
Key Takeaways
- Utilize the PSLQ algorithm for efficient integer relation searches.
- Apply number-theoretic filters to enhance search capabilities.
- Leverage discovered relations to create longer mathematical identities.
- Consider the implications of low Lehmer measures in your calculations.
How It Works
The framework combines the PSLQ integer-relation algorithm, which identifies integer relations among real numbers, with number-theoretic filters that exploit the structure of Gaussian integers. This synergy allows for a more efficient search for low-measure relations, significantly reducing computational complexity.