The Riemann hypothesis [+1/(n^ s)as n goes to infinity ] has to do with if you have a function zeta of a prime number if the zeros of that function [besides negative 2.-4, -6 ...] all are on a vertical line x=1/2/ and that is all part of number theory. my question is how would that same question apply to prime ideals? prime ideals are groups, not numbers and their main trait is anything in the larger group [that they are a part of] that is multiplied by that prime ideal stays inside it --and it is prime [no two smaller ideals multiplied together make it up]
I mean to say that much has been done with prime ideals but has anyone thought to look at them from the aspect of Riemann? After all there is a lot in common with algebraic ideals and numbers.
So maybe here too is connection?[Maybe even some answer about the Riemann hypothesis?]
[To see the connection between the zeta function and algebraic groups let me just mention that the only way that you evaluate the Riemann function is by extending it into the imaginary plane by means of the "i" and the "i" acts like a unitary matrix that rotates the vector, but leaves it's length untouched.]
[i would surprized if some mathematician had no thought of this since to me it seems so obvious. After all, a main idea of Riemann was to show the the zeta function with a complex "s" [i.e. + n^s as n goes to infinity] equals a product of primes. That is exactly the same construction you use for prime ideals.
