Introduction
What could be the deeper mathematics behind dualities?
Correspondence along common rationals and canonical identification: two manners to relate real and p-adic physics
Brief summary of the general vision
Quantum arithmetics and the notion of commutative quantum group
Quantum arithmetics
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Canonical identification for quantum rationals and symmetries
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More about the non-uniquencess of the correspondence between p-adic integers and their quantum counterparts
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The three options for quantum p-adics
Do commutative quantum counterparts of Lie groups exist?
Quantum counterparts of special linear groups
Do classical Lie groups allow quantum counterparts?
Questions
Quantum p-adic deformations of space-time surfaces as a representation of finite measurement resolution?
Could one understand p-adic length scale hypothesis number theoretically?
Number theoretical evolution as a selector of the fittest p-adic primes?
Only Option I is considered
Orthogonality conditions for SO(3)
Orthogonality conditions for SO(3)
Number theoretic functions rk(n) for k=2,4,6
What can one say about the behavior of r3(n)?
How quantum arithmetics affects basic TGD and TGD inspired view about life and consciousness?
What happens to p-adic mass calculations and quantum TGD?
What happens to TGD inspired theory of consciousness and quantum biology?
Appendix: Some number theoretical functions
Characters
Divisor functions
Class number function and Dirichlet L-function
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