Zeta Function and dual rate quantization.

This has become a favorite function in physics. It tells the physicist how many integer counts he will need if something quantizes down at the rates -s.

So,if I am delivering apples and the apples in my truck drop by 2/3 everytime I make a delivery. How many deliveries can I make. The mathematicians find bounds on this, like Einstein wanted to know how many integer units of energy was would a large number of things have if their energy was reduced per quant by -s. That tells him the lowest sample rate (temperature) he needs to get the integer down to one. The infinite sum, to the nearest integer tells us how many separable groups can form using that particular quant. Of course, separable groups are the primes, relative to the quant rate s.

Here is a fun way to handle the problem.

Replace n with a base two that raises in powers by some constant reals r,s, and j,k counting integer such that:


(r*j-s*k) is the exponent in base 2. When the difference is nearly zero then the j and k have counted to an integer,n, and the power of their product is n^2.

Pick the largest n you want, and make sure it is in the form:

2^M  -1, then 2^(-M) is the largest deviation in error from integers you will see, as long as you count fractions. Once your largest N is chosen, then pick the maximum j and k that match that number within precision.  Their ratio is their quantization rate.

Then count down in twos, in sorted order. If j is the slower counter, your number will count count as: 1,2,3,4,5,... with fractions in units of 1/2,1/3,1/4,1/5. Count as far as you like, go top to bottom, bottom to top; have fun. But this has little to do with primes and much more to do spacing out the integers evenly with respect to two operators.