There is an isomorphism of with in which . Find the element in to which must correspond for .
After arriving at an answer, I noticed that I said there was no answer for all of the even m values, so I'm not sure if I am correct.
To figure out the isomorphism, I used the example in the problem,
I reasoned that , in which that 1 corresponds to the exponent of zeta.
I used this to look for the other values asked in the problem.
For m=0, , but , so I said that for m=0, there is no corresponding zeta function.
For m=3 (skipping ahead), , , so .
I think I'm doing something incorrectly. Because since this is an isomorphism, and therefore a one-to-one correspondence, shouldn't all m=0,1,2,3,4,5,6 in map to a member of ? My method is producing answers for only the odd numbers.
Any help is extremely appreciated.