Introduction
What could be the deeper mathematics behind dualities?
Correspondence along common rationals and canonical identification: two manners to relate real and padic physics
Brief summary of the general vision
Quantum arithmetics and the notion of commutative quantum group
Quantum arithmetics

Canonical identification for quantum rationals and symmetries

More about the nonuniquencess of the correspondence between padic integers and their quantum counterparts

The three options for quantum padics
Do commutative quantum counterparts of Lie groups exist?
Quantum counterparts of special linear groups
Do classical Lie groups allow quantum counterparts?
Questions
Quantum padic deformations of spacetime surfaces as a representation of finite measurement resolution?
Could one understand padic length scale hypothesis number theoretically?
Number theoretical evolution as a selector of the fittest padic primes?
Only Option I is considered
Orthogonality conditions for SO(3)
Orthogonality conditions for SO(3)
Number theoretic functions r_{k}(n) for k=2,4,6
What can one say about the behavior of r_{3}(n)?
How quantum arithmetics affects basic TGD and TGD inspired view about life and consciousness?
What happens to padic 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 Lfunction
